EASY  LESSONS 


EASY  LESSONS 

IN 

PERSPECTIVE. 


INCLUDING 

INSTRUCTIONS 
FOR  SKETCHING  FROM  NATURE. 

"The  mo3t  consummate  master  is  tied  to  the  observation  of  every  one 
of  these  rules,  on  pain  of  pleasing  none  but  the  ignorant." 


BOSTON: 

BILLIARD,  GRAY,  LITTLE  AND  WILKINS. 
1830. 


DISTRICT  OF  MASSACHUSETTS,  to  wit  : 


District  Clerks  Office. 


Be  it  remembered,  That  on  the  sixth  day  of  October,  A.  D. 
1830,  in  the  fifty-fifth  year  of  the  Independence  of  the  United 
States  of  America,  Hilliard,  Gray,  Little  &  Wilkins,  of  the  said 
District,  have  deposited  in  this  Office  the  title  of  a  Book,  the 
right  whereof  they  claim  as  Proprietors,  in  the  words  following, 
to  wit : 

Easy  Lessons  in  Perspective.  Including  Instructions  for 
sketching  from  Nature.  "  The  most  consummate  master  is  tied 
to  the  observation  of  every  one  of  these  rules,  on  pain  of  pleasing 
none  but  the  ignorant." 

In  conformity  to  the  Act  of  the  Congress  of  the  United  States, 
entitled  "  An  Act  for  the  encouragement  of  Learning,  by  secur- 
ing the  copies  of  Maps,  Charts  and  Books  to  the  authors  and  pro- 
prietors of  such  copies,  during  the  times  therein  mentioned:" 
and  also  to  an  act  entitled  "  An  Act  supplementary  to  an  Act, 
(entitled,  An  Act  for  the  encouragement  of  Learning,  by  securing 
the  copies  of  Maps,  Charts  and  Books  to  the  authors  and  pro- 
prietors of  such  copies,  during  the  times  therein  mentioned ; 
and  extending  the  benefits  thereof  to  the  arts  of  designing,  en- 
graving, and  etching  liistorical  and  other  prints." 


TO 

JOHN  RAPHAEL  SMITH, 

THIS  BOOK 

IS  RESPECTFULLY  DEDICATED. 


■7 


PREFACE. 


It  is  the  object  of  this  book  to  explain  the  elements  of 
Perspective,  together  with  the  art  of  sketching  from  nature, 
in  a  familiar  manner,  so  as  to  render  them  intelligible  to  the 
young,  and  those  not  skilled  in  Mathematics  and  Geometry. 

There  are  many  learned  and  elaborate  treatises  on  Per- 
spective, but  they  are  generally  unintelligible  to  those  who 
cannot  command  the  assistance  of  a  teacher. 

The  subject  is  abstract  in  its  nature ;  an  acquaintance 
with  its  principles,  and  a  facility  in  its  practice,  cannot  be 
gained  without  attention  and  labour,  but  with  these,  it  is 
believed  that  any  one,  having  a  competent  skill  in  drawing, 
may  gain  from  this  book  all  the  knowledge  requisite  to 
sketch  from  nature  correctly. 


LESSONS 

IN 

PERSPECTIVE. 


LESSON  L 

LINES. 

A  straight  line  is  the  shortest  which  can  be  made 
between  two  given  points :  it  is  without  curve  or  bend, 
as  A,  Plate  1. 

Straight  hnes  are  horizontal,  perpendicular,  or  ob- 
lique. B,  is  a  horizontal  line  ;  C,  a  perpendicular  line; 
D,  E,  &  F,  are  oblique  lines. 

Parallel  lines  are  alike,  and  keep  the  same  distance 
from  each  other.    A  and  B  are  parallel  hnes. 

ANGLES. 

An  angle  is  formed  by  two  straight  lines  which  meet 
at  a  point.  G  R  is  an  acute  angle  ;  H,  an  obtuse  angle  ; 
I,  a  right  angle  ;  J,  a  triangle.  A  triangle  has  three 
sides,  and  three  corners  or  angles. 

An  angle  is  the  space  included  in  any  of  these  lines. 

The  size  of  an  angle  is  measured,  not  by  the  length 
of  its  lines,  but  by  the  space  included  in  them,  and  is 
accordingly  that  portion  of  a  circle  which  this  space 
contains. 

2 


2 


LESSONS   IN  PERSPECTIVE. 


A  circle,  whether  large  or  small,  is  by  geometricians 
divided  into  360  parts,  called  degrees.  A  degree, 
therefore,  is  not  any  precise  measure,  as  an  inch,  a  foot, 
or  a  mile,  but  simply  the  three  hundred  and  sixtieth 
part  of  any  circle.  In  a  large  circle,  the  parts  or  de- 
grees are  larger  lhan  in  a  small  one.  but  the  number  is 
the  same  (see  Plate  2,  circles  A  and  D.)  A  hne  which 
passes  through  the  centre  of  a  circle,  and  divides  it  in 
two  equal  parts,  is  called  a  diameter.  Thus  the  half 
of  the  small  circle  A,  divided  by  the  diameter  B,  is  180 
degrees,  as  truly  as  the  half  of  the  larger  circle  D. 

Any  straight  Hne  drawn  from  the  centre  of  a  circle 
to  the  circumference,  is  called  a  radius.  In  the  circle 
A  are  two  radii  E  and  F,  proceeding  from  the  centre  ; 
one  a  perpendicular,  the  other  a  horizontal  line.  These 
two  lines  include  one  quarter  of  the  circle  or  90  degrees. 
This  is  a  right  angle.  If  the  circle  were  larger,  as  D, 
a  right  angle  would  be  but  one  quarter  of  it.  There- 
fore a  right  angle  is  a  quarter  of  a  circle,  that  is,  90 
degrees,  if  it  extend  a  thousand  feet,  or  even  to  the 
heavens,  for  its  size  is  estimated  only  by  the  portion  of 
a  circle  which  it  includes.  This  is  an  idea  of  propor- 
tion, not  of  actual  measured  space,  and  it  is  important 
to  perceive  and  maintain  the  distinction.  An  angle 
which  includes  a  portion  of  a  circle  less  than  90  degrees, 
is  called  an  acute  angle,  and  may  be  of  any  size  from 
90°  to  almost  nothing.  As  E  G  (circle  A,  Plate  2) 
which  is  about  45  degrees,  and  H  F  which  is  not  more 
than  10  degrees. 

An  angle  which  includes  a  portion  of  a  circle  larger 
than  90  degrees,  is  called  an  obtuse  angle,  and  may  in- 
clude any  number  of  degrees,  from  90°  to  180°,  as 
K  J  (circle  D)  which  is  135°,  or  K  L  which  155°. 


LESSONS   IN  PERSPECTIVE. 


3 


LESSON  II. 

PLANES. 

Planes  cannot  be  so  well  described  as  lines  and 
angles.  Any  even  flat  surface  considered  without  re- 
gard to  its  tliickness,  is  a  plane.  A  table  is  a  plane,  the 
floor  is  a  plane,  the  side  of  the  house,  &lc. 

Planes  are  perpendicular,  horizontal,  or  oblique. 

The  wall  of  the  house  is  a  perpendicular  plane.  The 
floor  is  a  horizontal  plane,  and  so  is  the  ceiling  a  hori- 
zontal plane,  parallel  with  that  of  the  floor. 

Any  even  surface  which  varies  or  inclines  from  the 
perpendicular,  is  an  inclined  plane ;  as  a  writing  desk. 

A  perpendicular  plane  is  at  right  angles  with  a  hori- 
zontal plane.  Thus,  if  you  place  a  book  upright  on  a 
table,  the  book  is  a  perpendicular  plane,  and  the  table 
a  horizontal  one,  and  they  make  a  right  angle. 

An  inclined  plane  makes  an  angle  less  than  a  right 
angle,  with  a  horizontal  or  perpendicular  one.  For  a 
writing  desk,  which  is  an  inclined  plane,  does  not  make 
a  right  angle  with  the  table  on  which  it  stands,  as  the 
book  when  placed  upright  does  ;  but  it  makes  a  smaller 
angle,  and  this  angle  is  more  or  less  acute  (that  is,  small)  . 
according  to  the  greater  or  less  inclination  of  the  desk. 

Two  or  more  similar  planes  are  said  to  be  parallel. 

Planes  may  be  of  any  extent,  large  or  small.  Some 
really  exist,  as  the  floor  or  wall  of  a  house,  and  some 
are  only  imagined  to  exist,  for  the  purposes  of  science. 

If  two  balls  (M  and  N  Plate  2)  were  suspended  from 
a  ceiHng  by  cords  of  the  same  length,  and  were  revolv- 
ing about,  they  would  be  said  to  move  in  the  same  plane, 
though  no  plane  or  surface  were  actually  under  them; 
we  know  that  if  one  were  put  under  them,  they  would 
both  touch  it.  Thus  objects  are  said  to  be  in  the  same 
plane,  when  they  are  neither  higher  nor  lower  than 
each  other. 


4 


LESSONS   IN  PERSPECTIVE. 


All  objects  situate  on  the  earth  are,  in  perspective^ 
said  to  be  on  the  same  plane,  called  the  ground  plane. 

There  are  three  planes  especially  to  be  attended  to 
in  perspective,  viz. 

The  ground  plane,  the  horizontal  plane,  and  the 
perspective  plane. 

The  ground  plane  is  that  on  which  the  objects  to  be 
drawn  stand  ;  as  trees,  houses,  figures,  he. — And  when 
drawing  an  interior,  the  floor  of  the  room  is  a  ground 
plane. 

The  horizontal  plane,  is  an  imaginary  plane,  sup- 
posed to  extend  from  the  eye  of  the  spectator,  to  the 
verge  of  the  horizon. 

The  perspective  plane  is  also  imaginary.  It  is  a 
transparent  plane,  hke  a  window  or  pane  of  glass,  placed 
between  the  spectator  and  the  landscape,  or  object  to 
be  drawn,  standing  perpendicularly.  If  the  appearance 
of  objects  seen  through  this  plane,  were  traced  on  it, 
as  it  might  be  on  a  window  through  which  you  were 
looking,  it  would  make  a  correct  drawing  or  picture  of 
the  view. 

The  paper  on  which  you  draw,  in  taking  a  view,  is 
the  representative  of  this  perspective  plane  : — Could 
you  hold  it  up  in  a  perpendicular  position,  and  see- 
through  it,  as  you  do  through  a  window,  you  would 
draw  the  objects  beyond  it  correctly.  But  as  this  is 
impossible,  you  imagine  it  to  be  the  case. 


LESSON  III. 

VISION. 

All  objects  are  seen  by  means  of  rays  of  light  pro- 
ceeding from  them  to  the  eye.  ^ 
These  rays  proceed  in  straight  lines. 


LESSONS   IN  PERSPECTIVE. 


5 


As  they  come  in  all  directions,  from  every  side  of 
the  object,  and  enter  so  small  a  place  as  the  pupil  of 
the  eye,  it  is  evident  they  must  converge  or  draw 
together,  as  in  figure  O,  Plate  3.  Having  this  idea 
fixed  and  familiar  in  your  mind,  you  will  understand 
that,  whether  the  eye  be  nearer  to  or  farther  from  the 
object,  the  rays  must  converge  to  it ;  they  therefore 
form  an  angle  or  cone  whose  apex  or  point  is  the  eye, 
and  whose  base  is  the  size  of  the  object. 

Now  it  is  plain  that  the  size  of  this  angle  will  depend 
on  the  distance  of  the  object  from  the  eye.  When 
near,  the  angle  is  larger  than  when  the  object  is  far- 
ther off. 

Thus  the  rod  P  makes  a  smaller  angle  at  Q  than  at 
R,  and  the  angle  is  still  smaller  at  S. 

For  an  angle,  as  has  been  already  explained,  (see 
Lesson  1,  Plate  2,)  is  a  portion  of  a  circle,  and  if  you 
take  one  side  of  the  angle  for  a  radius,  viz.  semi-diam- 
eter, and  draw  a  circle,  making  the  apex  of  the  angle 
the  centre  of  the  circle,  it  will  then  be  seen  how  many 
degrees  of  this  circle  the  angle  occupies,  and  this 
shows  the  size  of  the  angle. 

To  ascertain  the  size  of  an  angle,  it  is  only  necessary 
to  draw  a  quarter  of  a  circle,  that  is,  a  right  angle, 
(when  the  angle  to  be  measured  does  not  exceed  ninety 
degrees,  or  a  right  angle).  Take  one  side  of  the  angle 
for  a  radius,  as  either  T  R,  T  Q,  or  T  S,  (Plate  3,) 
draw  from  the  corner  T  a  line  perpendicular  to  it.  The 
angle  R  T  P  it  will  be  seen,  is  more  than  half  that  quar- 
ter, or  about  50°  ;  at  Q  the  rod  makes  an  angle  of  23°, 
while  at  S  it  makes  less  than  one  fifth  of  a  right  angle, 
or  170. 

This  difference  in  the  size  of  the  angles  is  caused  by 
a  difference  of  distance.  The  size  of  the  rod  and  the 
position  of  the  eye  remaining  the  same  in  each  instance. 

This  is  called  the  angle  under  which  an  object  is 
2* 


6 


LESSONS   IN  PERSPECTIVE* 


seen.  It  is  the  angle  which  the  two  external  rays  of 
light  fronn  an  object  make  in  coming  to  the  eye. 

Though  somewhat  technically  expressed,  it  means 
nothing  more  than,  that  the  greater  the  distance  of  an 
object,  the  smaller  it  looks. 

In  perspective,  a  line  is  always  regarded  as  perpen- 
dicular to  another,  when  it  is  at  right  angles  with  it. 
Thus,  u  is  a  line  perpendicular  to  v,  or  v  to  u,  (Plate  3,) 
because  it  makes  a  right  angle,  i.  e.  an  angle  of  90 
degrees  with  it. 

It  has  been  said  that  we  see  objects  by  means  of 
rays  of  light  proceeding  from  them  to  the  eye,  and  that 
these  rays  converge,  and  form  an  angle  or  cone  of 
rays,  whose  apex  is  in  the  eye. 

The  side  of  a  house  w,  (Plate  4,)  is  seen  by  rays 
coming  from  it  to  the  eye.  The  two  exterior  rays 
form  an  angle,  viz.  a  If, 

In  drawing  a  house,  (or  other  object,)  you  may  imag- 
ine the  perspective  plane  to  be  situate  any  where, 
between  the  house  and  the  eye,  as  at  x  or  y.  The 
true  drawing  will  be  where  the  rays  of  light  coming 
from  the  house,  enter  (that  is,  intersect)  the  perspective 
plane  in  their  progress  to  the  eye. 

This  point,  where  the  rays  pass  through  the  perspec- 
tive plane,  is  called  the  seat  of  their  representation.  2 
in  the  perspective  plane  y,  and  3  in  the  perspective 
plane  x,  (Plate  4,)  are  the  seat  of  representation  for 
the  rays  abode  and  /,  proceeding  from  the  house  w. 

It  will  be  perceived  that  when  the  perspective  plane 
is  near  the  eye,  as  at  the  object  must  be  drawn 
smaller,  than  when  it  is  farther  off,  as  at  x. 

This  rule  must  not  be  confounded  with  the  one 
already  given,  (see  Plate  3,)  that  the  angle  under  which 
an  object  is  seen,  diminishes  in  proportion  to  the  dis- 
tance of  the  object ;  for  this  regards  the  apparent  size 


LESSONS   IN  PERSPECTIVE. 


7 


of  an  object,  determined  by  its  distance  from  the  eye  ; 
but  the  other,  only  the  drawing  of  the  object,  deter- 
mined by  the  situation  of  the  perspective  plane. 

Objects  are  drawn  under  their  true  angles,  and  pre- 
serve their  relative  proportions,  whether  the  perspective 
plane  is  near  or  more  remote  ;  as  appears  from  the 
figure,  (Plate  4.)  The  house  at  ?/,  is  seen  and  drawn 
under  the  same  angle  as  at  and  the  same  proportion 
of  the  windows  and  spaces  between,  is  preserved  in 
each. 

For,  take  1,2  for  a  radius,  and  draw  a  circle  or 
right  angle,  and  you  will  perceive  that  the  house  is 
seen  under  an  angle  of  20°.  So  take  I  3,  or  1  4  ra- 
dius, the  circle  is  larger,  but  the  size  of  the  angle  (that 
is,  the  number  of  degrees)  is  the  same. 

The  angle  under  which  a«  object  is  seen,  determines 
the  size  and  nearness  to  the  eye. 

It  will  also  be  perceived,  that  the  distance  of  the 
perspective  plane  from  the  eye  is  important;  and  having 
been  once  fixed,  must  not  be  varied  in  the  same  view. 

To  illustrate  this  still  more,  place  a  card  between 
the  eye  and  an  object,  a  house  or  tree  for  instance,  if 
the  card  is  held  near,  say  within  a  foot  of  the  eye,  it 
will  cover  or  hide  the  object,  and  if  it  were  transparent, 
this  object  could  be  traced  on  the  small  space  of  a  card 
of  two  or  three  inches  size.  But  hold  the  same  card 
twice  or  three  times  as  far  off,  and  it  will  not  cover 
half  the  former  object;  and  if  you  drew  on  the  card  at 
that  distance,  you  could  not  get  all  of  the  object  in. 
Tiiis  card  represents  the  imaginary  perspective  plane 
on  which  objects  are  drawn,  and  by  this  experiment  you 
can  understand,  that  when  it  is  near  you,  you  can  put 
more  on  the  same  space  than  when  it  is  farther  off, 
though  each  object  in  the  view  will  preserve  the  same 
relative  proportions  in  both  cases. 


8 


LESSONS  IN  PERSPECTIVE. 


LESSON  IV. 

HORIZON  LINE,  AND   GROUND  LINE. 

The  horizontal  plane  in  perspective,  is  a  plane 
imagined  to  extend  from  the  eye  of  the  beholder  to  the 
horizon,  or  farthest  verge  of  the  earth  which  the  eye 
can  reach,  viz.  where  the  sky  appears  to  touch  the 
earth. 

Suppose  the  perspective  plane  interposed  between  the 
eye  and  the  view,  (like  a  window,  as  has  been  already 
described,  see  Lessons  2  and  3,)  the  horizontal  plane 
would  intersect  it,  or  cut  it  through  at  right  angles,  and 
the  line  formed  on  the  perspective  plane,  by  this  inter- 
section is  the  horizon  line. — What  is  called  the  horizon 
line  on  the  paper  or  picture,  is  the  representation  of  this 
line.  For  if  you  suppose  the  perspective  plane  set 
upright  on  the  ground  before  you,  higher  than  your 
eye  ;  then  the  horizontal  plane,  to  reach  from  your  eye 
to  the  verge  of  the  sky,  must  pass  through  the  perspec- 
tive plane,  and  thus  make  a  line  exactly  parallel  with 
the  top  and  bottom  line  of  your  perspective  plane. 

Then  draw  such  a  line  on  your  paper,  and  ;;his  is 
your  horizon  line.  You  will  find,  when  sketching,  that 
some  particular  point  of  a  tree  or  window  of  a  house 
comes  just  against  it.  The  meeting  of  the  sky  with 
the  earth,  and  the  distant  hills  will  also  be  on  this  line. 

It  is  evident  that  the  height  of  this  line  (viz.  how  far 
it  is  above  the  bottom  line  of  the  picture)  depends  on 
the  height  of  the  eye  :  and  this  is  the  case  whether  the 
spectator  is  standing  or  sitting, — is  on  the  top  of  a 
house,  or  mountain,  or  on  the  plain. 

Could  an  actual  plane  extend  from  the  eye  to  the 
horizon,  lines  situate  on  the  ground  plane  or  earth 
would  be  under  it,  and  the  ground  plane  would  appear 
to  meet  it  in  the  horizon,  and  be  inclined  to  it ;  making 


LESSONS   IN  PERSPECTIVE. 


9 


with  it  an  angle,  whose  size  would  be  determined  by 
the  height  of  the  spectator.  This  is  what  is  meant  by 
the  phrase,  "  having  a  high  cr  a  low  horizon."  The 
figures  A  B  and  C  (Plate  4)  are  of  about  the  same 
height.  Their  horizon  varies  in  consequence  of  the 
difference  in  their  position. 

Lines  being  here  necessarily  used  to  express  planes, 
the  explanations  are  less  clear  than  in  experimental 
teaching.  Let  E  be  a  table,  which  is  a  horizontal 
plane,  representing  the  ground  plane  on  which  the  spec- 
tator and  also  the  objects  to  be  drawn  stand,  A,  a  small 
figure  stationed  at  one  side  of  the  table,  representing  the 
spectator, — D,  another  horizontal  plane,  parallel  to  the 
table,  placed  just  as  high  as  the  eye  of  the  figure  A. 
Then  the  plane  D,  would  represent  the  horizon  plane. 
Now,  if  you  had  on  the  table  objects  to  be  drawn,  models 
of  houses,  trees,  &c. — and  threads  attached  to  the  top 
and  bottom  of  these  objects,  were  brought  through  the 
eye  of  the  figure  A,  after  the  manner  of  rays  of  light ; 
you  would  perceive,  that  the  grjDund  plane  appears  to 
the  eye  to  rise  till  it  meets  the  horizon  plane  in  the 
distance. — As  E  rises  to  meet  D,  and  the  angle  these 
two  planes  make,  as  D  E  with  figure  A,  or  D  E  with 
figure  B,  or  with  C  (Plate  4)  depends  on  the  height 
and  position  of  the  figures  ABC,  viz.  the  beholder. 

The  more  distant  the  object,  the  higher  up  on  the 
perspective  plane,  and  the  smaller  they  appear.  If,  for 
instance,  the  perspective  plane  were  a  window,  the  base 
of  a  house  or  tree  near  it  would  be  seen  through  the 
panes  at  the  bottom  ;  while  that  of  a  similar  object  a 
mile  or  two  off,  would  be  seen  through  the  upper  panes, 
or  those  more  nearly  on  a  line  with  the  eye. 

When  you  begin  to  take  a  view,  you  first  fix  your  po- 
sition, which  must  be  stationary,  and  determine  on  the 
height  of  your  eye,  and  on  the  distance  at  which  the 
perspective  plane  is  to  be  placed  or  imagined,  keeping 


10 


LESSONS  IN  PERSPECTIVE. 


in  mind  that  your  paper  is  the  representation  of  the 
perspective  plane.  Then  draw  a  line  at  the  bottom  of 
the  picture  G,  (Plate  5,)  which  is  called  the  ground 
line,  and  is  the  line  formed  by  the  intersection  of  the 
perspective  plane,  with  the  original  ground  plane;  or  in 
in  other  words,  a  line  where  the  perspective  plane  rests 
on  the  earth.  This  ground  line  is  the  boundary  of  the 
bottom  of  the  picture  ;  for  the  nearest  object  or  point 
which  you  design  to  include  in  your  picture,  must  be 
on  the  ground  line."^ 

Having  drawn  your  ground  hne,  then  draw  the  hori- 
zon line  H  parallel  with  it,  at  the  height  of  your  eye  ; 
which  line  represents  the  place  where  the  sky  meets 
the  earth. 

The  space  D  between  these  two  lines  represents  the 
ground  plane,  or  the  earth  on  which  objects  stand. 
The  nearer  an  object  is  to  the  spectator,  the  lower  down 
it  will  be  on  the  ground  plane.  I  is  nearer  than  J,  and 
J  than  K.  (Plate  5.) 

Remember  that  it  is  only  such  lines  as  are  nearer  the  ' 
'  ground  plane  than  the  eye,  that  are  drawn  under  the  • 
horizon  line.  On  looking  at  a  tree  or  house,  or  any 
object  taller  than  yourself,  you  look  down  to  see  the 
base,  and  you  look  up  to  see  the  top  ;  consequently  the 
base  is  below  the  horizontal  plane,  and  the  top  is  above 
it.  If  you  had  three  objects  to  draw  at  different  dis- 
tances, as  I  J  K,  (Plate  5,)  the  base  of  each  would  be 
situate  on  the  ground  plane  according  to  its  distance, 
while  the  top  would  come  above  the  horizon  line. 
The  more  distant  an  object  is,  the  smaller  it  looks.  K 

*  It  is  best  not  to  include  in  the  picture  any  large  object  nearer  . 
than  100  feet,  and  even  a  small  object,  as  a  carriage,  house,  or  man 
at  that  distance,  would  occupy  a  considerable  portion  of  a  perspec- 
tive plane,  situate  ten  or  fifteen  feet  from  the  eye.  Of  this  you  may 
be  easily  convinced,  by  looking  out  at  a  window  placed  at  this  dis- 
tance from  the  eye,  and  observing  how  large  a  portion  of  it  such 
small  objects  when  very  near  will  occupy. 


LESSONS  IN  PERSPECTIVE. 


u 


and  J  are  not  so  far  above,  nor  so  far  below  the  horizon 
line  as  I ;  this  expresses  at  once  that  they  are  farther 
off. 


LESSON  V. 

POINT  OF  SIGHT.      PARALLEL  PERSPECTIVE. 

There  is  a  point  in  the  horizon  line  exactly  opposite 
to  the  eye  ;  which  is  called  the  point  of  sight.  It  is 
very  important  in  perspective. 

It  is  usually  placed  near  the  centre  of  the  picture; 
but  it  may  be  on  either  side,  according  to  the  position  of 
the  beholder.  You  can,  if  you  choose,  put  the  objects 
on  each  side  of  you,  into  your  picture ;  and  then  the 
point  of  sight  will  be  in  or  near  the  centre  ;  but  if  you 
wish  to  drav/  only  what  is  on  one  side,  and  omit  the 
other;  then  the  point  of  sight  will  be  near  the  extremity 
of  the  picture  ;  because  the  object,  which,  in  the  position 
you  have  taken,  is  opposite  your  eye,  is  the  one  at 
which  you  will  end  your  view. 

The  trees  (Plate  5,  L)  are  all  on  the  left  side  of  the 
spectator,  and  he  must  stand  at  B,  opposite  to  S,  to  see 
them  as  they  are  drawn  here ;  and  if  he  choose  to  omit 
the  objects  on  the  other  side,  S  will  be  his  point  of 
sight,  at  the  extremety  of  the  picture. 

If  he  prefer  to  take  in  the  objects  on  his  right,  he  will 
have  his  point  of  sight  in  the  centre  of  his  picture.  As 
the  picture  M,  (Plate  5,)  where  S  is  the  point  of  sight; 
because  in  this  view  are  included  the  houses  on  the 
right,  as  well  as  the  trees  on  the  left  of  the  spectator. 
Thus  you  perceive  that  you  can  have  the  point  of  sight 
wherever  you  please  :  provided  it  be  on  the  horizon 
line,  and  opposite  the  spectator. 


12 


LESSONS  IN  PERSPECTIVE. 


The  point  of  sight  then  is  the  point  in  the  farthest 
distance,  exactly  opposite  the  eye  of  the  beholder,  and 
is  always  on  the  horizon  line.  Its  use  may  be  illustrated 
by  the  drawing  of  a  house. 

This  is  usually  a  square  or  rectangular  figure  :  sup- 
pose it  to  stand  exactly  before  you,  opposite  your  eye. 
It  will  then  be  correctly  expressed  by  horizontal  lines 
for  the  top  and  bottom,  and  perpendicular  hues  for  the 
sides  or  wall.  Its  place  on  the  ground  plane,  is  deter- 
mined by  its  distance  from  the  perspective  plane.  You 
will  see  the  front,  but  nothing  of  either  of  the  other 
sides  :  as  N.  (Plate  5.) 

But  if  the  house  is  placed  a  little  to  the  right  or  left 
of  the  spectator,  one  end  can  be  seen  as  well  as  the 
front. — Look  at  a  house  from  these  two  different  posi- 
tions. 

(Plate  6)  R.  That  part  a  of  the  end  seen,  adjoin- 
ing the  front,  and  next  the  spectator,  is  nearer  than  the 
part  6,  adjoining  the  back  ;  therefore  a  must  look  larger 
than  h.  As  this  side  (a  h)  actually  recedes  from  the 
eye,  it  must  be  drawn  diminishing  in  size,  after  the 
following  manner. 

Having  drawn  the  front  R,  (Plate  6)  exactly  as  in 
N,  (Plate  5)  excepting  that  it  is  farther  removed  from 
the  point  of  sight, — draw  tw^o  lines,  one  from  the  top, 
the  other  from  the  bottom  of  the  house,  meeting  in  the 
point  of  sight  5,  w^hich  is  the  vanishing  point,  or  that 
where  all  the  lines  on  this  side,  parallel  with  the  top 
and  bottom,  would  meet. 

The  lines  for  the  doors,  windows,  &;c.  meet,  that  is, 
vanish  in  this  point. 

When  a  house,  or  other  rectangular  object,  stands 
square  before  you,  and  not  cornerwise  or  obliquely,  two 
sides,  viz.  the  front  and  back,  are  parallel  with  the 
ground  line,  and  the  other  two  are  exactly  at  right 
angles  with  it. 


LESSONS  IN  PERSPECTIVE. 


13 


Lines  which  in  the  original  object  are  parallel  with 
the  ground  line,  are  drawn  parallel.* 

Lines  at  right  angles  with  the  ground  line,  vanish  or 
terminate  in  the  point  of  sight. 

Perpendicular  lines  which  are  parallel  with  the  per- 
spective plane,  like  the  sides  of  a  house,  are  drawn  per- 
pendicular and  parallel. 

Parallel  lines  (whether  horizontal  like  the  top  and 
bottom  lines  of  the  front  of  the  house,  in  Plate  6,  R,  or 
perpendicular,  like  the  sides  of  the  same  house)  are 
shorter  than  their  originals,  in  proportion  to  their  dis- 
tance from  the  perspective  plane.  Thus  the  top,  bottom, 
and  sides  of  R,  though  parallel,  like  their  originals,  are 
shorter  ;  because  they  are  at  some  distance  from  the 
perspective  plane,  and  the  beholder.  And  if  the  house 
were  farther  off  they  would  be  still  shorter,  in  exact 
proportion  to  their  distance;  which  means  no  more  than 
that  the  house  would  look  smaller,  if  it  were  father  off. 
Still,  however,  they  preserve  the  same  direction,  and 
are  parallel  like  their  originals  ;  but  the  lines  on  the  side 
a  b  are  smaller  than  their  originals,  and  they  take  a 
different  direction ;  instead  of  being  drawn  parallel, 
like  their  originals,  they  tend  to,  and  meet  in  the  point 
of  sight. — In  parallel  perspective  therefore,  there  are 
but  three  sorts  of  lines  to  be  considered. 

J  St.  Those  which  are  parallel  with  the  ground  'line, 
and  are  horizontal  lines  in  a  pfcture.  2d,  Those  which 
are  parallel  with  the  perspective  plane,  and  are  perpen- 
dicular Hnes  in  the  picture.  3d,  Those  which  are  at 
right  angles  with  the  ground  line,  and  when  drawn,  vanish 
in  the  point  of  sight.  The  length  of  all  these  lines,  that 
is,  how  much  smaller  they  are  than  their  originals,  de- 
pends on  their  distance. 

This  is  parallel  perspective,  and  these  rules  comprise 

*  Original  lines  are  such  as  really  exist  in  contradistinction  to  the 
<lrawing  of  them. 

3 


14 


LESSONS   IN  PERSPECTIVE. 


all  that  is  requisite  for  the  sketching  of  rectangular  fig- 
ures, placed  parallel  with  the  spectator.  Further  instruc- 
tions for  the  drawing  of  circles  and  curves  in  parallel 
perspective,  will  be  found  in  the  lessons  on  circles, 
bridges,  and  interiors,  he. 

In  taking  a  view  out  of  doors,  you  will  be  able  to 
determine  the  apparent  size,  situation,  and  relative  pro- 
portions of  objects,  with  sufficient  accuracy,  by  holding 
up  a  pencil  or  ruler  before  your  eye,  in  a  horizontal 
and  perpendicular  position,  and  comparing  the  object 
with  this  measure.  If  you  nearly  close  your  eyes  while 
looking,  it  will  facilitate  the  operation  ;  for  if  you  look 
at  a  house  with  your  eyes  shut  as  near  as  can  be,  and 
see,  and  hold  a  pencil  before  them,  you  can  with  your 
finger  mark  exactly  how  much  of  this  measure  the 
house  occupies  to  your  eye.  By  looking  in  the  same 
way,  at  a  house  more  distant,  you  will  see  how  much 
less  of  the  pencil  this  occupies  than  the  first  5  you  have 
only  then  to  make  this  difference  in  their  sizes  when 
you  draw  them. 

By  the  same  method  you  can  form  a  correct  judg- 
ment, how  much  taller  one  tree  is  than  another,  or  than 
a  house  or  other  object ;  how  much  higher  one  hill 
rises  against  the  sky  than  another  ;  or  how  large  a 
space  a  sheet  of  water  occupies  on  your  ground  plane. 
This  space  for  water,  fields,  or  any  level  surface  on 
the  earth  or  ground  plane,  will  be  much  less  on  your 
picture,  than  you  would  believe,  till  you  have  made  the 
experiment,  and  measured  it  in  this  way.  You  may 
observe,  also,  that  the  hues  for  the  banks  of  rivers, 
lakes,  he.  vary  less  from  the  horizontal,  than  you 
would  be  disposed  to  draw  them,  if  you  judged  merely 
from  your  eye,  without  comparing  them  with  your 
measure,  or  some  horizontal  line. 

Observe  that  your  measuring  rule  or  pencil,  must  be 
held  at  the  same  distance  through  the  whole  sketch ; 


LESSONS  IN  PERSPECTIVE. 


15 


for  an  object  which  would  occupy  the  whole  at  a  dis- 
tance of  three  feet,  would  not  be  equal  to  half  of  it, 
when  held  near  the  eye. 

It  is  easy  to  preserve  the  same  distance  for  the 
measure,  by  means  of  a  cord  fastened  to  its  centre  and 
held  in  the  mouth. 

Novices  in  sketching,  are  often  at  a  loss  to  determine 
on  the  place  for  their  horizon  line,  and  think  that 
because  they  see  no  such  line  in  the  landscape  before 
them,  they  need  not  and  cannot  draw  one  ;  but  it  is 
difficult,  if  not  impossible,  to  get  a  correct  likeness 
without  one,  and  it  is  easy  to  determine  on  its  place. 

Suppose  you  were  out  of  doors,  and  looking  at  the 
view  4,  (Plate  6)  with  a  design  to  sketch  it. 

If  you  were  on  level  ground,  your  horizon  would  be 
low ;  and  the  horizon  line  must  be  drawn  about  as  far 
from  the  ground  line,  as  it  is  in  the  sketch, — wherever 
you  draw  it,  on  the  paper,  would  be  the  place  for  that  part 
of  the  picture,  where  the  sky  meets  the  earth.  Then 
observe  by  holding  up  a  pencil,  or  other  straight  stick 
in  a  horizontal  position,  exactly  at  the  height  of  your 
€ye,  what  this  line  passes  across.  The  distant  hill  6,  is 
on  the  right  hand,  and  there  is  another  hill  on  the  left ; 
consequently  S  between  them  is  opposite  your  eye,  and 
is  the  place  to  mark  the  point  of  sight  on  the  horizon 
line. 

The  hill  h  rises  a  little  above  this  line,  and  comes  a 
little  below  it, — the  hill  d  rises  higher  and  comes  farther 
down  on  the  ground  plane :  draw  them  so.  Then  notice 
the  cedar  tree  c, — two  thirds  of  it  are  above  the  horizon 
line,  (that  is,  two  thirds  of  it  appear  above  any  hne 
held  horizontally  across  your  eye,)  and  the  root  is  one 
third  below.  The  elm  tree  e  being  nearer  the  specta- 
tor, its  base  approaches  almost  to  the  ground  line, 
while  its  top  reaches  far  above  the  horizon,  to  the  top 


16 


LESSONS   IN  PERSPECTIVE. 


of  the  picture.  The  horizon  line  passes  near  the  inser- 
tion of  the  lowest  branch. 

Next  draw  the  house  /;  observe  where  the  base 
comes  above  the  foot  of  the  tree,  e,  the  horizon  line 
passes  near  the  middle,  just  above  the  lower  row  of 
windows ;  therefore  you  must  draw  these  windows 
below  the  line,  and  the  other  row  above  it. 

Thus  this  line  helps  you  to  ascertain  the  situation  of 
every  object  you  wish  to  draw, — and  the  observation  of 
the  relative  position  of  these  objects  enables  you  to 
determine  the  place  of  the  horizon  line. 

After  a  httle  practice,  and  with  the  help  of  these 
rules,  no  difficulty  can  be  experienced  in  sketching  any 
common  view  in  parallel  perspective. 

The  spectator  in  this  view  is  placed  at  J,  opposite  to  S. 

Lines  from  the  side  of  the  house,  to  the  point  of 
sight,  S,  determine  the  drawing  of  the  side  w,  which  is 
at  right  angles  with  the  ground  hne,  and  vanishes  in  the 
point  of  sight.  The  side  /  being  parallel  with  the 
ground  line,  must  be  drawn  parallel,  according  to  the 
rules  already  given. 

Throughout  the  book  the  following  references  are 
invariable  : — H,  horizon  hne  ;  G,  ground  line  ;  S,  point 
of  sight;  D,  point  of  distance. 


LESSON  VL 

OBLIQUE  PERSPECTIVE. 

Oblique  perspective  teaches  the  drawing  of  objects 
situated  obliquely  to  the  ground  line,  as  when  a  house 
or  other  object  stands  with  the  corner  towards  you,  like 
W,  (Plate  6). 

As  no  side  of  the  object  W  is  parallel  with  the  ground 
line  G,  no  lines  can  be  drawn  parallel  with  it  5  since  as 


LESSONS   IN  PERSPECTIVE. 


17 


has  been  said  in  lesson  5,  original  lines  parallel  with  the 
ground  line,  are  drawn  parallel  with  it,  but  no  others. 

Each  of  the  sides  makes  an  angle  with  the  ground 
line,  and  must  have  a  vanishing  point.  This  cannot  be 
the  point  of  sight,  that  being  the  vanishing  point  for 
such  lines  only  as  are  at  right  angles  with  the  ground 
line.  They  must  have  another  vanishing  point  or 
points. 

These  are  on  the  horizon  line,  and  are  thus  ascer- 
tained. 

Prepare  your  paper  as  before  with  a  ground  line  G, 
(Plate  7,  Figure  I,)  horizon  line  H,  and  point  of 
sight  S. 

Rule  a  perpendicular  hne  through  the  point  of  sight : 
this  is  called  the  prime  vertical  line.  Mark  on  this 
line  the  point  D,  called  the  point  of  distance. 

This  space  from  S  to  D,  represents  the  distance  of 
the  spectator  from  the  perspective  plane  :  in  other 
words,  the  distance  at  which  you  stand  when  taking 
a  sketch,  from  the  nearest  object  you  intend  to  put  into 
your  picture.  It  may  be  arbitrary,  but  the  distance  here 
marked  is  a  good  proportion.  It  is  rather  more  than 
twice  the  distance  from  the  ground  Hne  to  the  horizon. 
If  you  refer  to  Lesson  3,  Plate  4,  you  will  see  the  use 
and  importance  of  the  distance  point.  The  distance  D 
(Plate  7,  Figure  I)  is  set  off,  or  marked  on  the  prime 
vertical  line.  In  other  cases,  which  will  be  hereafter 
explained,  it  is  measured  on  the  horizon  line. 

Having  proceeded  thus  far,  look  at  the  building,  if 
you  are  sketching  one,  and  estimate  as  well  as  you  can 
(by  means  of  your  measuring  stick  held  in  a  horizontal 
position)  the  angle  which  the  bottom  Hne  makes  with 
the  ground  line,  and  draw  this  from  the  ground  hne  to 
the  horizon  G  V.  Where  it  intersects  the  horizon  at  V, 
is  the  vanishing  point  for  this  side.  Draw  a  Hne  from 
3* 


18 


LESSONS   IN  PERSPECTIVE. 


the  point  of  distance  D,  to  the  vanishing  point,  mak- 
ing D  V. 

Draw  the  line  D  W  so  as  to  make  up  the  comple- 
ment of  a  right  angle  ;  that  is,  if  the  first  line  D  V 
make  an  angle  of  60^  with  the  vertical  line,  let  the 
second  D  W  make  an  angle  of  30°  ;  or  if  one  is  45° 
let  the  other  be  45°,  both  being  equal  to  90°,  and  D  V 
and  D  W  form  a  right  angle. 

If  you  have  not  the  necessary  instruments  at  hand  for 
taking  angles,  you  can  easily  obtain  a  right  angle,  by 
cutting  a  bit  of  card  exactly  square,  place  one  side  on 
the  line  D  V,  letting  the  corner  touch  the  point  D  ;  then 
the  other  side  will  give  you  the  line  which  you  are  to 
produce  from  D  to  the  horizon,  to  find  the  point  W  for 
the  vanishing  point  of  the  second  side  of  the  building. 

If  the  object  you  are  drawing  is  rectangular,  the  hues 
to  determine  its  vanishing  points  must  form  a  right 
angle. 

The  point  W  is  the  vanishing  point  for  the  second 
side  of  the  house,  and  for  all  lines,  as  doors,  or  win- 
dows on  it. 

Determine  the  nearest  point  in  the  base  of  the  house, 
as  A,  by  your  eye,  or  measure.  The  line  A  V  for  the 
first  side  of  the  house  is  already  drawn.  Draw  the 
other  side  to  its  vanishing  point,  making  A  W. 

Raise  the  perpendicular  A  B  I  to  the  height  the 
house  appears  to  be.  A  little  practice  will  enable  you 
to  judge  of  this  height,  with  sufficient  accuracy  for  all 
the  purposes  of  sketching.  Compare  it  with  the  objects 
in  the  view,  or  compare  the  height  with  the  length. 
Draw  C  and  F  from  the  point  I  to  their  vanishing 
points  V  and  W. 

Draw  the  perpendiculars  L  and  M,  determine  their 
place  by  your  eye  and  the  aid  of  your  measuring  stick. 

Observe  that  windows  and  other  parts,  diminish  in 
apparent  size  as  they  are  drawn  nearer  the  vanishing 


LESSONS  IN  PERSPECTIVE. 


19 


point.  This  rule  applies  also  to  the  vanishing  side,  in 
parallel  perspective,  viz.  the  v^^indows,  doors,  he.  of 
that  side  which  vanishes  in  the  point  of  sight.  The  eye 
is  generally  sufficiently  correct  to  judge  of  this  propor- 
tion ;  but  the  lessons  in  drawing  from  a  ground  plan 
will  very  much  assist  the  scholar,  who  after  having 
studied  them,  will  be  in  possession  of  the  principle  upon 
which  they  are  diminished,  and  can  apply  it  with  ease 
to  any  case,  without  making  all  the  measurements  re- 
quired in  drawing  from  a  ground  plan. 

The  point  of  the  roof  E,  which  in  the  original,  is 
exactly  over  the  centre  of  that  side,  must  in  the  drawing 
be  placed  a  little  beyond ;  because  that  half  which  is 
farthest  from  the  spectator,  appears  smaller  than  the 
other. 

Further  directions  for  drawing  roofs  will  be  given  in 
Lesson  9. 

The  Hne  E  V  for  the  top  of  the  roof  vanishes  at  V, 
because  it  is  parallel  with  the  bottom  line  of  the  house  ; 
and  so  would  all  the  lines  for  the  doors  and  windows, 
parallel  with  the  base  hne.  These  are  omitted,  in 
order  that  the  figure  may  not  be  too  complicated. 

If  there  are  several  buildings  in  the  view  you  wish  to 
take,  some  standing  parallel,  others  oblique,  you  need 
not  be  puzzled  by  this  circumstance,  but  regard  them 
as  so  many  different  sketches.  Thus,  Plate  7,  Figure 
2,  N  O  P  are  three  houses  standing  in  different  posi- 
tions, O  is  parallel,  N  and  P  oblique. 

Having  drawn  the  ground  line,  horizon  line,  point  of 
sight,  prime  vertical  line,  through  it  and  the  point  of 
distance  ;  draw  the  parallel  house  O,  the  end  q  vanish- 
ing in  the  point  of  sight,  because  it  is  at  right  angles 
with  the  ground  line. 

The  house  N  must  have  two  vanishing  points  of  its 
own,  (R  and  g,  on  the  horizon  line,)  because  it  stands 
obliquely.    These  are  to  be  found,  as  already  directed, 


20 


LESSONS   IN  PERSPECTIVE. 


in  the  house  above,  figure  1,  and  the  lines  for  the  top, 
the  roof,  and  the  doors  or  windows,  must  all  be  ruled 
to  these  vanishing  points  ;  for  these  lines  are  in  the 
original,  parallel  with  the  base  line  of  the  house,  and 
lines  which  are  parallel,  if  they  vanish,  have  the  same 
vanishing  point. 

Having  found  the  vanishing  point  for  one  side,  noth- 
ing is  easier  than  to  draw  all  parallel  lines  on  that  side 
to  this  point.  You  cannot  fail  of  getting  them  right  by 
this  rule  ;  whereas  if  you  trust  to  your  eye  alone,  it 
would  be  scarcely  possible  that  your  drawing  should  be 
correct. 

The  house  P  standing  obliquely,  must  also  have 
its  own  vanishing  points,  found  as  already  directed,  by 
means  of  the  distance  point  D  on  the  vertical  hne,  and 
making  the  complement  of  a  right  angle  of  both  sides. 
These  points  are  V  for  the  side  T,  that  for  the  side  P 
extends  beyond  the  plate.  This  often  happens  in 
oblique  perspective,  therefore  the  paper  must  be  larger 
than  the  picture,  and  the  horizon  hne  extended  far 
enough  beyond  the  boundary  of  the  picture,  to  receive 
the  vanishing  points.  The  side  which  makes  the 
smallest  angle  with  the  ground  line,  is  that  whose  van- 
ishing point  will  be  farthest  from  the  point  of  sight.  If 
it  makes  a  very  small  angle,  that  is,  stand  nearly  square, 
this  vanishing  point  will  be  very  remote,  and  the  lines 
of  that  side  will  be  almost  parallel.  In  this  case,  the 
vanishing  point  for  the  other  side  will  be  very  near  to 
the  point  of  sight,  and  vanish  more  suddenly.  You 
will  see  less  of  this  side,  or  rather  the  representation  of 
it,  will  take  up  less  space  in  the  drawing  than  the  other. 

This  can  be  easily  proved  by  drawing  houses  with 
various  degrees  of  obliquity,  according  to  the  foregoing 
rules  ;  which  will  be  very  useful  practice. 


LESSONS   IN  PERSPECTIVE. 


21 


LESSON  Vll. 

GROUND   PLAN,   OR  ICHNOGRAPHY.  PARALLEL 
PERSPECTIVE. 

If  you  desire  great  accuracy  in  your  view,  or  have 
occasion  to  draw  from  description,  you  will  make  use 
of  a  ground  plan.  This  is  called  taking  the  ichno- 
graphy  of  objects. 

First  make  a  scale  or  measurement,  divided  into 
equal  parts,  in  which  inches,  or  parts  of  inches  are  taken 
for  feet  or  other  dimensions.  As  A,  (Plate  8)  which 
is  a  scale  of  40  feet,  or  other  measures. 

Adhere  to  your  scale  in  all  your  measurements  for 
the  same  picture. 

Draw  the  ground  line,  horizon  line,  vertical  line,  and 
point  of  sight. 

Measure  the  distance  at  which  the  spectator  is  sup 
posed  to  stand  from  the  perspective  plane,  and  set  it 
off  in  this  instance,  on  the  horizon  line,  from  S.  The 
point  D  thus  ascertained  is  the  distance  point.  Its  use 
will  presently  appear.  It  is  necessary  to  keep  in  mind, 
what  has  already  been  explained  of  the  perspective 
plane,  viz.  that  it  is  imaginary,  and  represented  by  the 
paper  on  which  you  draw,  that  it  is  a  transparent  plane 
held  up  before  the  eye,  at  some  distance,  on  which  you 
delineate  the  objects  beyond,  as  they  are  seen  through 
it ;  and  that  the  drawing  of  each  part  or  point  is  pre- 
cisely where  the  rays  of  light  pass  through  it,  in  their 
passage  from  the  object  to  the  eye.  Though  not  visi- 
ible  as  straight  lines,  these  rays  actually  move  in  straight 
lines,  and  form  an  image  of  the  picture  in  the  eye, 
where,  small  as  this  image  is,  the  relative  proportions  of 
every  part  are  exactly  preserved. 

It  is  desirable  for  one  who  is  learning  perspective,  to 
know  something  of  the  theory  of  vision,  and  a  few  hours 


22 


LESSONS  IN  PERSPECTIVE. 


Study  of  any  treatise  on  optics,  with  a  plate  of  the  eye, 
would  be  sufficient  for  the  acquisition  of  all  the  knowl- 
edge requisite. 

The  objects  to  be  drawn  are  always  beyond  the 
perspective  plane,  that  is,  this  plane  is  between  these 
objects  and  the  eye ;  the  nearest  point  coming  just  up 
to  the  plane,  and  the  place  where  this  nearest  object 
comes,  is  the  place  for  the  ground  line.  All  this  has 
been  repeatedly  said,  but  it  is  necessary  to  call  it  to 
mind,  and  render  the  ideas  famiHar  by  repetition,  that 
what  follows  may  be  fully  understood.  If  the  objects 
to  be  drawn  are  beyond  the  perspective  plane,  they 
may  be  at  different  distances,  and  it  has  been  already 
explained,  that  the  lines  of  light  coming  from  the  object 
to  the  eye  form  an  angle,  the  size  of  which  depends  on 
the  size-  of  the  object,  and  its  distance  from  the  eye. 
The  drawing  of  it  is  also  affected  by  the  distance  of 
the  perspective  plane  :  see  Lesson  3.  Now  if  you 
make  the  object  of  the  same  size  and  distance  from  the 
eye,  and  put  the  perspective  plane  in  the  same  place 
as  the  original,  (that  is,  the  same  proportion,  measuring 
by  a  scale,)  you  will  obtain  the  same  angle  as  the  origi- 
nal makes,  and  this  angle  will  intersect  the  perspective 
plane  precisely  as  the  original  angle  would  a  pane  of 
glass,  at  the  given  distance  from  the  eye. 

The  use  of  a  ground  plan  is  to  give  these  proportions 
and  angles,  with  perfect  accuracy,  and  of  course  to 
enable  you  to  obtain  a  correct  drawing  of  any  object 
thus  described  and  laid  down. 

It  may  be  the  case,  that  you  cannot  place  yourself 
at  a  convenient  distance  from  the  object  you  wish 
most  to  include  in  your  sketch  ;  but  you  may  imagine 
yourself  there. 

With  a  ground  plan  you  can  select  any  distance, 
which  the  situation  of  the  objects  warrants ;  and  if  you 
adhere  to  your  points  of  distance,  sight,  &ic.  and  your 


LESSONS  IN  PERSPECTIVE. 


23 


measurements,  the  drawing  will  always  be  in  good  per- 
spective. 

Having  fixed  the  distance  point  on  the  horizon  line 
D,  you  proceed  to  draw  a  plan  of  the  object.  Let  B 
(Plate  8)  represent  the  ground  floor  of  a  house,  meas- 
ured accurately  by  your  scale,  and  placed  at  the  same 
distance  from  the  ground  line  as  the  original.  Carry 
up,  or  as  it  is  expressed  technically,  produce  the  two 
lines  N  O  and  K  J,  till  they  intersect  the  ground  line. 
These  lines  are  at  right  angles  with  the  ground  line, 
and  therefore  vanish  in  the  point  of  sight. 

From  F  and  I,  the  points  of  their  intersection,  draw 
two  lines  to  the  point  of  sight,  making  I  S  and  F  S  ; 
I  S  is  the  true  representation  of  I  O  and  F  S  of  F  J. 

Measure  the  distance  at  which  the  house  stands  from 
the  ground  line,  viz.  from  K  to  F,  and  set  this  off  on 
the  ground  line  from  the  point  of  intersection  F  to  M, 
and  then  the  actual  size  of  that  side,  and  set  it  off  to  L, 
M  L  being  equal  to  K  J  ;  from  the  points  M  and  L 
draw"  two  lines,  meeting  in  the  point  of  distance  D, 
making  the  angle  M  D  L,  which  angle  is  precisely  the 
same  that  two  rays  of  light  would  make,  proceeding 
from  an  object  of  the  same  dimensions  as  that  in  the 
plan,  and  at  the  same  distance  from  the  eye  and  the 
perspective  plane.  The  space  F  K  influencing  the 
size  of  the  angle  precisely  in  the  same  degree,  when 
•  transferred  to  the  ground  line  at  F  M,  as  it  would  do  in 
the  original. 

Suppose  a  perspective  plane,  and  an  object  of  the 
same  dimensions  as  B,  placed  at  the  same  distance 
beyond  it,  that  B  is  now  placed  before  the  perspective 
plane  in  Plate  8.  Let  the  eye  be  stationed  in  front, 
just  as  high  above  the  ground  line,  as  S  the  point  of 
sight  is,  and  at  the  same  distance  from  the  perspective 
plane,  that  D  is  from  S.  Two  threads  from  the  side 
K  J,  carried  in  straight  lines  to  the  eye,  as  rays  of  light 


24 


LESSONS  IN  PERSPECTIVE. 


come,  would  form  this  same  angle  at  M  D  L,  and 
would  pass  through,  or  intersect  the  perspective  plane 
in  their  passage  to  the  eye,  exactly  at  the  points  h  and  a. 
These  are  the  points  required,  and  give  the  apparent 
size  on  the  perspective  plane,  of  that  side  which  is  at 
right  angles  with  the  ground  line,  and  vanishes  in  the 
point  of  sight. 

h  is  the  point  which  corresponds  to  K,  rule  h  d  par- 
allel with  the  ground  line,  which  represents  N  K. 
Then  from  the  other  point  o,  rule  a  c,  which  answers 
to  O  J,  and  the  figure  is  complete  ;  a  b  c  d  being  the 
true  drawing  of  K  J  N  O. 

From  the  points  d  b  and  a  raise  perpendicular  lines 
for  the  sides  or  walls  of  the  house.    In  order  to  ascertain 
the  apparent  height,  raise  a  perpendicular  from  the 
point  I,  this  is  the  point  at  which  the  line  O  N,  when 
produced,  intersects  the  ground  line ;  for  could  the  house 
be  moved  up  to  the  perspective  plane,  it  would  touch 
it  at  I  F.    Measure  on  this  perpendicular,  by  means 
of  your  scale,  the  actual  height  of  the  house  (of  which 
it  is  presumed  you  have  on  your  plan  an  exact  des- 
cription) set  this  off,  from  I  to  m,  from  u  rule  u  S, 
which  intersects  the  perpendicular  d  e,  at  e,  this  gives 
the  apparent  height. — You  ascertain  by  this  process 
precisely  how  much  the  house  diminishes,  in  conse- 
quence of  its  distance  N  I  from  the  perspective  plane. 
Rule  ef  parallel  with  d  b,  because  these  lines  are  in 
the  original  parallel  with  the  ground  hne.    Rule  /,  S, 
which  being  parallel  with  b  a,  has  the  same  vanishing 
point.    The  perpendicular  from  c,  which  would  com- 
plete the  four  walls  of  the  house,  is  not  drawn,  because 
it  is  not  seen. 

The  height  of  the  roof  is  set  off  from  u  to  v.  Draw 
w  at  the  true  angle,  viz.  making  the  same  angle  with 
the  line  e  f  as  in  the  original.  Draw  v  S  ;  where  it 
intersects  at  x  is  the  apparent  height  for  the  roof.  The 


LESSONS   IN  PERSPECTIVE. 


25 


point  y,  which,  in  the  original  is  the  centre  of  that  side, 
appears  a  little  beyond,  in  the  perspective  representa- 
tion, because  the  half  of  this  side  which  is  farthest  off 
looks  smallest.  To  ascertain  the  precise  place,  divide 
M  L  exactly  in  halves  at  rule  a  hne  from  z  to  the 
distance  point  D.  Where  this  intersects  at  g  raise  a 
perpendicular  till  it  intersects  the  line  a?  y  at  y;  this 
gives  the  place  y  for  the  centre.  For  h  a  correspond 
with  M  L,  and  g  with  z. 

If  the  house  were  nearer  the  ground  line,  or  farther 
off,  you  would  proceed  as  above  ;  only  remember  to 
produce  the  two  lines  which  are  at  right  angles  with  the 
ground  line,  (as  O  N  and  J  K,)  till  they  touch  the 
ground  line,  and  rule  them  to  the  point  of  sight.  Set  off 
the  distance  F  K,  whatever  it  may  be  on  the  ground 
line,  as  F  M ;  and  from  M  set  off  the  true  measure- 
ment of  the  side  at  right  angles,  viz.  K  J.  This  is  the 
side  which  vanishes  in  the  point  of  sight,  and  therefore 
is  next  the  point  of  sight. 

If  the  plan  B  were  on  the  other  side  of  the  point  of 
sight,  then  ONI  would  be  laid  down  or  measured  off 
on  the  ground  hne,  as  F  M  L  are  now. 

This  figure  is  a  sufficient  rule  for  the  drawing  of  any 
rectangular  building,  placed  parallel  or  square  before 
you,  let  the  dimensions  and  distance  be  what  they  may  ; 
provided  these  are  accurately  laid  down  on  the  ground 
plan. 


LESSON  VIII. 

GROUND   PLAN.     OBLIQUE  PERSPECTIVE. 

If  you  wish  to  put  a  house,  or  other  figure,  in  oblique 
perspective,  by  a  ground  plan,  you  first  prepare  your 
paper  with  the  ground  hne,  horizon  hne,  point  of  sight, 
4 


26 


LESSONS   IN  PERSPECTIVE. 


and  prime  vertical  line  through  it,  and  the  distance 
point,  set  off  on  the  vertical  line  from  the  point  of  sight, 
as  in  Lesson  6.  Leave  space  enough  below  the  ground 
line  to  draw  your  plan,  of  the  same  dimensions,  position 
and  distance  as  the  original  :  see  Plate  9,  O. 

Obtain  the  vanishing  points  A  and  B  by  means  of 
parallels  ruled  from  the  distance  point  D,  on  the  vertical 
line  to  the  horizon,  D  B  being  parallel  with  d  b,  and 
D  A  with  d  a. 

Produce  the  lines  which  mark  the  four  sides  of  the 
house,  d  b  c,  c  a,  a  d,  till  they  intersect  the  ground 
hne. 

At  the  points  of  intersection  efgh,  rule  lines  to  the 
vanishing  points.  A  is  the  vanishing  point  for  the  line 
a  d  g,  and  therefore  for  c  b  A,  because  they  are  parallel; 
and  you  must  keep  in  mind  the  rule,  viz.  parallel  lines 
if  they  vanish,  have  the  same  vanishing  point,  fdb  and 
e  a  c  are  parallel  and  vanish  at  B;  therefore  make  e  B 
and/B.  The  intersection  of  these  lines  on  the  per- 
spective plane,  make  the  figure  ij  k  Z,  which  is  the 
perspective  representation  of  a  d  b  c  m  the  plan  :  be- 
cause, these  points  of  intersection  on  the  perspective  plane 
are  the  same  which  would  be  made  by  the  rays  of  light 
coming  from  the  points  in  the  original  to  the  eye,  pro- 
vided the  dimensions  and  position  correspond  to  those 
in  the  plate,  as  has  been  shown  in  Lesson  7. 

From  the  points  kj  Z,  raise  perpendiculars  for  the 
sides  or  walls  of  the  house. 

Ascertain  their  height  by  the  following  method  :  Rule 
perpendicular  hnes  from  the  points  of  intersection,  with 
the  ground  line  g  and  /.  If  you  look  back  to  Lesson 
7  you  will  find  you  did  the  same  thing,  and  the  reason 
is  there  given,  excepting  that  there  you  ruled  one  line, 
whereas  here  you  have  two.  As  has  been  said  in  a 
former  lesson,  oblique  perspective  is  twice  as  much 


LESSONS   IN  PERSPECTIVE. 


27 


work  as  parallel,  because  both  sides  have  a  vanishing 
point. 

On  these  perpendiculars  raised  from  g  and/,  measure 
by  means  of  your  scale,  the  actual  height  from  the 
ground  line. 

Thus  if  the  side  a  c  is  thirty  feet,  and  the  height  of 
the  house  forty,  make  /  m  and  g  m  one  third  more 
than  a  c. 

Rule  the  lines  m  B  and  m  A  ;  they  intersect  on  the 
perpendicular  k,  giving  the  top  of  the  wall  for  each 
side.* 

The  point  of  the  roof  n  is  exactly  over  the  centre  of 
the  house  O,  in  the  ground  plan  ;  to  find  which,  rule 
diagonals  across  the  perspective  representation  of  the 
floor  of  the  house,  making  i  k  and  i  j.  These  lines 
cross  at  the  centre  o  which  represents  O  in  the  plan.f 

From  0  raise  a  perpendicular  o  n.  Produce  m  to  P, 
which  is  the  height  of  the  roof:  rule  from  this  to  its 
vanishing  point  making  P  B,  where  it  intersects  at  n  is 
the  point  of  the  roof,  rule  lines  from  n  to  the  corners  of 
the  house. 

If  the  roof  is  not  pointed,  rule  the  lines  for  the  ridge 
to  their  vanishing  points.  In  the  original,  they  are 
parallel  with  the  top  and  bottom  lines  of  the  house,  and 
therefore  vanish  at  A  and  B. 

If  much  accuracy  is  required,  measure  the  space  to 
be  cut  off  from  the  peak  on  the  line  m  P,  and  by  ruling 
from  this  to  the  vanishing  point,  you  get  the  precise 
place  for  the  ridge. 

*  The  line  m  g  is  not  drawn  all  the  way,  but  only  at  its  com- 
mencementj  at  m.  n  o  is  not  carried  beyond  S,  as  these  lines  come  so 
near  those  for  the  nearest  window. 

I  By  producing  the  lines  5  7  and  6  8  (Plate  9)  to  the  ground  line, 
and  ruling  them  to  their  vanishing  points,  as  you  have  done  the 
outside  lines  ad,  d  b,  &c.,  you  will  find  the  centre  as  truly  as  by 
ruling  the  diagonals  i  k  and  I  j ;  but  this  last  method  is  more  simple. 


28 


LESSONS   IN  PERSPECTIVE. 


% 


Divisions  for  the  doors  and  windows  are  ascertained, 
as  may  be  seen  from  the  Plate,  by  being  marked  on  the 
ground  plan,  produced  to  the  ground  line,  and  then 
ruled  to  the  vanishing  point  A. 

From  the  points  at  which  these  lines  intersect  the 
base  lines  of  the  house,  raise  perpendiculars,  which  will 
give  the  perspective  place  for  all  the  windows  and 
doors. 

For  as  the  sides  of  the  house  recede,  the  farther 
part  looks  smaller  than  the  nearer,  and  you  perceive 
that  the  method  given  shows  this  gradation  with  ex- 
actness. 

When  the  ground  plan  is  so  large  that  the  lines  to  be 
produced  to  the  ground  line  (as  c  b  produced  to  h) 
would  extend  beyond  the  paper,  and  thus  be  inconvenient 
to  draw,  the  following  method  of  making  divisions,  or 
measuring  lines  may  be  used  ;  and  perhaps  it  will  be 
thought  preferable  in  every  case  where  there  is  a  ground 
plan.  If  you  wish  to  find  J  (the  representation  of  the 
point  b)  on  the  line  k  B,  (Plate  9)  which  is  the  point 
where  the  house  terminates,  lay  your  ruler  from  the 
distance  point  D,  on  the  prime  vertical  line,  to  the  point 
b  in  the  plan,  making  D  6. — You  perceive  that  it  cuts 
the  line  k  B  (which  is  the  base  line  of  the  house)  at  J, 
precisely  as  the  line  from  A  to  A,  and  answers  the  pur- 
pose of  measurement  equally  well.  And  if  you  lay  the 
ruler  from  D  to  a,  you  get  the  point  /,  previously  obtain- 
ed by  ruling  a  line  from  e  to  B. 

In  the  same  manner  places  for  the  windows  may  all 
be  found,  by  ruling  lines  from  D  to  1  2  3  4,  which 
lines  are  not  drawn  on  the  Plate,  to  avoid  confusion. 

The  angles  are  the  same  in  the  last  method  as  the 
first,  and  both  correspond  exactly  with  the  angles,  which 
rays  of  light  proceeding  from  the  house  to  the  eye  (of 
the  given  dimensions  and  position)  would  make  :  see 
Lesson  15. 


0 


LESSONS  IN  PERSPECTIVE. 


29 


A  t^ird  method  of  marking  divisions  in  oblique  per- 
spective, somewhat  more  intricate  than  either  of  the 
above,  but  which  dispenses  with  the  necessity  of  a 
ground  plan,  will  be  given  in  the  Lesson  on  bridges. 


LESSON  IX. 

FURTHER  INSTRUCTIONS   FOR  ROOFS. 

In  giving  the  true  slant  to  all  the  lines  of  a  roof,  no 
two  of  which  are  drawn  parallel,  a  knowledge  of  the 
rules  of  perspective  is  requisite  ;  and  this  knowledge 
cannot  be  acquired  without  some  labour,  especially 
when  the  pupil  is  learning  from  books  ;  the  constant 
reference  to  plates,  making  the  process  far  more  tedious 
than  when  he  has  the  assistance  of  a  teacher.  It  is  the 
object  of  this  work  to  enable  those  who  cannot  obtain 
the  services  of  a  teacher,  to  acquire  a  knowledge  of 
perspective  by  their  own  efforts.  But  it  is  not  pre- 
tended, that  this  mode  of  learning,  can  be  made  as  easy, 
or  even  as  intelligible,  as  the  instructions  of  a  competent 
teacher. 

The  rules  now  to  be  explained,  belong  more  properly 
to  a  future  lesson,  but  their  application  to  the  drawing 
of  roofs  is  here  given,  because  this  is  necessary  to 
render  the  instructions  for  drawing  a  house  complete. 

In  Plate  7,  figure  I  is  a  house  B,  standing  obliquely ; 
V  and  W  are  the  vanishing  points  for  the  two  sides. 
It  will  be  remembefi'ed,  that  a  perpendicular  line  ruled 
through  the  point  of  sight,  as  D  S  in  this  figure,  is  called 
the  prime  vertical  line.  It  represents  a  ray  of  light 
coming  straight  from  the  perspective  plane  through  the 
eye,  and  marks  the  point  of  sight  as  S,  and  also  the 
distance  of  the  spectator  as  D,  and  it  is  plain  that  the 


30 


LESSONS   IN  PERSPECTIVE. 


farther  off  the  spectator  is  placed  from  the  perspfctive 
plane,  the  longer  would  be  this  ray. 

The  learner  must  not  be  puzzled  by  the  situation  of 
this  line  in  the  plate.  If  a  spectator  were  actually 
placed  before  a  window,  a  ray  of  light  coming  straight 
from  the  object  exactly  opposite  his  eye,  through  the 
perspective  plane  or  window  wouldT  be  a  horizontal 
line,  and  not  perpendicular,  as  it  is  in  this  figure.  But 
such  a  line  cannot  be  expressed  on  a  flat  sheet  of  paper, 
nor  is  this  necessary  ;  for  the  angle  under  which  an 
object  is  seen,  and  the  distance  of  the  perspective  plane, 
can  be  measured  with  the  same  accuracy  when  they 
are  laid  down  on  a  flat  sheet ;  as  is  done  in  Plate  7, 
and  this  is  all  that  is  requisite  to  obtain  a  correct  per- 
spective representation. 

This  subject,  however,  will  be  further  illustrated  in 
Lesson  15.  To  return  to  the  prime  vertical  line,  figure 
1,  Plate  T.  This  ray  coming  straight  to  the  eye,  on 
which  the  distance  D  is  marked,  is  sometimes  called  the 
visual  ray.  A  similar  line  drawn  through  the  vanishing 
points  of  oblique  planes,  (viz.  sides  of  houses,  he. 
standing  obliquely,)  as  W  in  this  figure,  is  the  vertical 
line,  or  visual  ray  for  these  points,  called  also  the 
radial  or  vanishing  line. 

Therefore  the  line  drawn  through  W,  viz.  W  X,  and 
through  V,  figure  2,  Plate  7,  are  the  radials,  or  van- 
ishing lines  of  these  same  points  W  and  V.  The  roof 
of  the  house  in  figure  1,  Plate  7,  is  a  prism,  whose 
base  vanishes  at  W  and  V,  and  its  sides  must  vanish  at 
some  point  on  the  radial  of  one  or  the  other  of  these 
points,  as  X.  This  point  is  deterR:;ined  by  the  angle 
of  the  slant  line  with  the  base,  as  E  I,  which  being  pro- 
duced, till  it  intersects  the  radial,  gives  the  vanishing 
point  X,  to  which  point  draw  the  other  line  for  the 
roof,  as  g  ;  for  g  being  parallel  to  E  1,  must  if  it  van- 
ishes, have  the  same  vanishing  point.    All  lines  have 


LESSONS  IN  PERSPECTIVE. 


31 


a  vanishing  point,  except  such  as  lie  on  planes,  parallel 
with  the  perspective  plane  or  the  ground  line.  The 
wall  of  a  house  which  stands  parallel  or  square  before 
you,  is  a  plane  parallel  with  the  perspective  plane,  or 
the  window  through  which  you  look  ;  but  the  roof  is 
not,  it  makes  an  angle  more  or  less  large,  with  the 
perspective  plane,  consequently  any  lines  lying  on  it, 
(viz.  the  outline  of  the  roof,)  have  a  vanishing  pointy 
found  according  to  the  directions  given  above. 

In  figure  2,  Plate  7,  the  roof  of  the  house  P  vanishes 
at  y,  (see  figure  1,)  on  the  the  radial  of  its  own  vanish- 
ing point  V,  that  is,  on  the  perpendicular  drawn  through 
V,  and  the  point  y«is  ascertained  by  producing  the  line 
of  the  roof  r  to  y. 

In  the  house  O,  standing  parallel,  the  peak  of  the  roof 
is  ascertained,  by  finding  first,  the  centre  of  the  ground 
floor  of  the  house.  This  ground  floor  is  an  oblong  rec- 
tangular figure,  the  perspective  appearance  of  which 
may  be  found  without  the  aid  of  a  ground  plan. 

From  the  point  j?,  rule  a  line  to  the  point  of  sight, 
which  will  give  the  end  not  seen,  parallel  with  and 
through  the  upper  corner  of  q  rule  a  horizontal  line, 
and  you  have  the  floor  of  the  house,  as  it  would  appear 
if  the  house  were  transparent,  and  you  could  see  it  all. 
To  find  the  centre,  rule  diagonals  from  each  corner, 
and  the  point  of  their  intersection,  as  you  see  by  the 
figure,  is  the  apparent  centre.  Raise  a  perpendicular 
from  this  centre  to  the  height  required,  and  you  have 
the  point  h  for  the  roof:  let  the  slant  lines  meet  here, 
and  cut  them  off  by  ridge  poles  if  required. 

The  roof  of  the  house  N  (Plate  7)  is  obtained  in  the 
same  way,  by  drawing  a  radial  through  R,  one  of  its 
vanishing  points. 

In  Plate  8  the  house  is  parallel,  and  the  vanishing 
point  for  the  roof  is  found  on  the  prime  vertical  line, 
because  the  base  of  this  roof,  viz.  the  line  /  S  vanishes 
in  S,  the  point  of  sight. 


32 


« 

LESSONS  IN  PERSPECTIVE. 


LESSON  X. 

CIRCLES. 

A  circle  may  be  circumscribed  by  a  square,  and  if 
tliis  square  is  put  into  perspective,  the  circle  can  be 
drawn  v;ithin  this  perspective  representation,  or  if  accu- 
racy is  required,  the  square  can  be  divided,  and  the 
corresponding  parts  in  the  representation  will  be  a  suf- 
ficient guide  for  drawing  the  circle.  The  larger  the 
circle  is,  and  the  greater  the  degree  of  accuracy  re- 
quired, the  more  numerous  must  be  the  divisions  of  the 
square,  put  into  perspective.  All  this,  however,  is  only 
putting  into  perspective,  horizontal,  perpendicular,  or 
oblique  lines  :  the  rules  for  doing  which,  have  been 
fully  given. 

But  as  some  difficulty  may  be  found  in  applying  these 
rules  to  new  cases,  the  following  illustrations  are  offered. 

Plate  10,  figure  1,  represents  a  circle  put  into  paral- 
lel perspective. 

H,  horizon  line  ;  S,  point  of  sight ;  D,  point  of  dis- 
tance ;  G,  ground  line,  sometimes  in  works  on  perspec- 
tive, called  intersection  line,  because  it  is  the  line  form- 
ed by  the  intersection  of  the  perspective  plane  with  the 
ground  plane. 

The  circle  C,  in  the  ground  plan  is  circumscribed  by 
a  square,  diagonals  and  diameters  are  ruled.  The 
points  at  which  the  diagonals  strike  the  circumference, 
make  equal  divisions  on  the  circumference,  though  not 
on  the  square.  Through  these  points  are  ruled  lines, 
called  sines  and  cosines. 

Put  all  these  lines  into  perspective,  according  to  the 
rules  already  given  in  Lesson  7 ;  this  being  a  case  in 
parallel  perspective. 

The  lines  A  B  F  E  L  must  be  produced  till  they 
intersect  the  ground  line  :  from  the  points  of  intersection 


LESSONS   IN  PERSPECTIVE. 


33 


rule  them  to  the  point  of  sight,  because  they  are  lines 
at  right  angles  with  the  ground  line. 

Measure  the  distance  of  the  circle  from  the  ground 
line,  viz.  M  L,  set  it  off  on  the  ground  line,  making  M 
N,  then  the  distances  of  the  points  K  and  I,  which  are 
equal  to  O  P ;  rule  lines  from  N  O  P  to  the  point  of 
distance  D.  The  object  of  these  lines  is  merely  to 
mark  the  perspective  size  of  the  square,  by  means  of 
the  points  of  their  intersection  with  the  line  M  S,  drawn 
to  the  point  of  sight ;  therefore  at  these  points  of  inter- 
section, rule  the  lines  u  v  t  parallel  with  the  ground 
line,  corresponding  to  A  L,  V  K,  W  I  in  the  ground 
plan. 

Rule  diagonals  through  the  points  r  t  u  w,  repre- 
senting the  diagonals  in  the  plan. 

Observe  the  points  of  intersection  in  the  perspective 
representation,  which  correspond  with  those  in  the  plan, 
and  draw  the  circle  through  them.  You  perceive  that 
the  perspective  circle  is  divided  into  parts  like  that  in 
the  plan,  but  in  the  former  they  are  not  equal,  although 
they  are  so  in  the  latter.  The  upper  half  of  the  circle 
is  smaller  than  the  lower  half;  this  circumstance  gives 
the  figure  a  peculiar  character,  which  you  will,  with 
a  httle  practice,  be  able  to  draw  with  sufficient  accuracy 
for  the  common  purposes  of  sketching,  without  all  these 
lines,  or  even  without  any,  although  you  never  could 
arrive  at  this,  except  by  a  knowledge  of  these  rules. 

Portions  of  circles,  as  arches,  doors  standing  more  or 
less  open,  (which  describe  portions  of  circles  on  the 
floor,  by  the  movement  which  opens  them,)  are  drawn 
on  the  same  principles,  and  will  be  further  illustrated. 

Plate  10,  figure  2  represents  two  circles  in  obhque 
perspective. 

The  ground  plan  is  first  made  ;  then  the  vanishing 
points  are  obtained  by  drawing  parallels.  From  the 
distance  point  D,  (which  in  obhque  perspective  is 


34 


LESSONS   IN  PERSPECTIVE, 


always  set  off  on  the  prime  vertical  line,)  draw  D  B 
parallel  with  c  W,  and  D  A  parallel  with  c  q.  The 
points  of  intersection  with  the  horizon  line,  give  A  B 
vanishing  points  for  the  sides  c  W  and  c  q. 

The  lines  c  K  L  M  W  are  produced  till  they  inter- 
sect the  ground  line,  also  c  e  N  f  q,  and  from  these 
points  of  intersection  lines  are  ruled  to  each  vanishing 
point.  O  A  P  ^  c  to  B,  and  R  T  w  V  to  A,  and  the 
circle  is  drawn  through  the  points  of  intersection  as  in 
the  original. 

As  the  line  W,  if  produced  to  the  ground  line  would 
extend  beyond  the  picture,  the  rule  is  laid  from  D  to 
W,  which  gives  the  point  y  with  equal  correctness  as  by 
the  other  method,  as  has  been  shown  in  Plate  9  :  see 
D  b  and  D  a. 


LESSON  XI. 

BRIDGES. 

It  is  nearly  impossible,  with  the  most  accurate  eye, 
in  taking  a  sketch,  to  draw  a  bridge  of  several  arches 
correctly,  without  a  knowledge  of  the  rules  of  per- 
spective ;  more  especially  if  the  bridge  stand  ob- 
liquely. 

The  following  method  with  the  figure  is  given,  to 
to  illustrate  the  application  of  the  rules  of  perspective  to 
the  drawing  of  bridges  ;  though  somewhat  elaborate,  it 
has  been  made  as  clear  and  simple  as  the  subject 
permits. 

If  this  figure  be  studied  faithfully,  and  the  rules 
applied  to  new  designs  made  by  the  pupil,  he  will  meet 


LESSONS   IN  PERSPECTIVE. 


35 


with  no  difficulty  afterwards,  in  sketching  with  sufficient 
accuracy,  without  the  necessity  of  laying  down  all  the 
lines  and  points  in  these  figures.  With  the  principles 
of  perspective  familiar  to  his  mind,  he  will  never  make 
any  glaring  mistakes,  even  in  the  most  rapid  and  care- 
less sketching  ;  while  without  this,  his  most  laboured 
productions  would  be  wanting  in  truth  of  expression. 
To  this,  every  one  acquainted  with  perspective,  will 
readily  assent. 

Plate  11  represents  abridge  in  oblique  perspective. 
Having  drawn  the  horizon  and  ground  lines,  points  of 
sight  and  distance,  rule  the  line  E  F,  making  the  angle 
with  the  ground  line,  which  you  presume  the  bridge  to 
make.  Of  this  you  will  judge  by  holding  up  your 
measuring  stick.  From  F  draw  F  D,  F  is  one  van- 
ishing point ;  draw  also  the  line  D  L  at  right  angles 
with  D  F,  which  gives  L  for  the  other  vanishing  point, 
(as  it  is  oblique,  both  sides  vanish.)  The  angle  F  D  L 
is  a  right  angle.  Select  by  your  eye,  with  the  aid  of 
the  measuring  stick  (described  in  Lesson  5)  the  nearest 
point  in  the  bridge  J,  raise  the  perpendicular  J  i  to 
the  height  at  which  the  bridge  appears  to  be  ;  which 
you  can  determine,  by  observing  how  near  it  comes  to 
the  horizon  :  then  rule  i  F  for  the  top,  because  the 
top  and  bottom  are  parallel,  and  must  have  the  same 
vanishing  point. 

Draw  a  line  through  the  point  J,  parallel  with  the 
ground  line  ;  set  off  on  this  line  the  measurement  of  the 
size  of  each  arch.  This  you  may  ascertain  by  com- 
paring the  size  of  the  nearest  arch  with  the  height  of 
the  bridge.  Perfect  accuracy  is  not  requisite,  but  the 
spaces  for  each  arch  must  be  equal.  You  thus  get  the 
points  J  K  M  N.  Measure  the  space  F  D,  (with  com- 
passes if  you  have  them,)  and  lay  it  on  the  horizon 
from  F,  by  describing  the  arc,  making  the  point  R. 


36 


LESSONS  IN  PERSPECTIVE. 


This  is  called  the  radius*  of  its  own  vanishing  point, 
and  answers  the  same  purpose  as  the  distance  point 
(set  off  on  the  horizon  from  the  point  of  sight,  in  paral- 
lel perspective)  for  taking  measurements. 

Rule  lines  from  the  points  K  M  N  to  R,  they  inter- 
sect the  line  for  the  bottom  of  the  bridge  J  F,  at  the 
points  O  P  Q,  and  give  the  apparent  size  of  each  arch, 
viz.  the  place  for  the  foot  of  each  arch.  Then  divide 
the  space  for  each  arch,  viz.  J  K,  K  M,  and  M  N 
equally,  and  rule  lines  from  these  divisions  to  R. 
These  lines  are  not  ruled  in  the  figure ;  they  intersect 
the  line  J  F  at  T  m  the  places  for  the  centre  of  each 
arch.  Raise  perpendiculars  from  t  u  v  to  the  top  hne 
of  the  bridge  :  draw  a  guide  line  A  F  for  the  tops  of 
the  arches,  which  line  being  parallel  with  the  top  and 
bottom  of  the  bridge,  has  the  same  vanishing  point. 

Draw  a  straight  line  from  each  of  the  points  W  X  Y, 
to  the  points  J  O  P  Q,  like  the  dotted  lines  in  the  plate. 
Describe  arches  on  these  lines.  The  arches  may  be 
drawn  without  these  straight  lines,  but  you  will  not 
probably  do  them  as  well. 

Draw  the  line  J  L,  which  gives  the  other  side  of  the 
bridge,  L  is  the  vanishing  point  for  all  lines  parallel  to 
J  L  ;  therefore  rule  O  L,  P  L,  and  Q  L,  which  lines 
represent  the  under  part  of  the  arch,  as  it  leaves  the 
water,  and  are,  as  you  will  perceive  by  a  little  observa- 
tion, parallel  in  the  original  bridge,  with  the  end  J  L. 

You  have  now  ascertained  the  direction  of  these 
lines,  but  not  their  size.    Each  arch,  as  you  observe  in 

*  A  radius  is  the  semidiameter  of  a  circle,  that  is,  a  straight  line 
drawn  any  where  from  the  centre  to  the  circumference.  If  you  take 
F  (Plate  il)  for  a  centre,  and  putting  one  foot  of  the  compasses  in 
this  point,  and  extending  the  other  to  D  for  the  size,  and  draw  a 
circle  ;  F  R  would  be  a  radius  of  this  circle,  as  well  as  F  D,  and  it 
is  called  the  radius  of  its  own  vanishing  point,  because  it  is  the 
radius  of  a  circle,  of  which  this  vanishing  point  F  is  the  centre,  and 
F  D  the  radius. 


LESSONS  IN  PERSPECTIVE. 


37 


the  figure,  shows  more  of  the  under  part,  as  it  recedes 
farther  from  R  its  distance  point.  Measure  by  the 
scale  you  have  used  for  your  other  measurements,  on 
the  line  J,  the  space  J  Z,  being  the  real  size  for  the  end 
of  the  bridge,  then  take  the  radius  of  the  vanishing  point 
of  this  side  L,  viz.  L  D,  (as  you  did  for  the  other  side,) 
and  lay  it  on  the  horizon  line  to  r,  making  L  r.  Rule 
Zr,  the  point  of  its  intersection  at  a  is  the  size  of  this 
end  ;  raise  a  perpendicular  at  a,  rule  i  L  parallel  with 
a  J,  in  the  original,  therefore,  having  the  same  van- 
ishing point ;  from  h  rule  b  F,  the  top  of  the  further  side 
parallel  with  i  F,  for,  as  the  whole  bridge  is  below  the 
horizon,  you  see  this  line,  otherwise  you  could  not. 
Rule  a  line  from  a  to  the  vanishing  point  F,  this  line 
represents  the  base  line  of  the  further  side  of  the  bridge, 
parallel  in  the  original  with  J  F,  therefore  having  the 
same  vanishing  point.  The  hues  for  the  under  part  of 
the  arches,  viz.  O  L,  PL,  Q  L,  are  already  drawn. 
a  F  intersects  these  at  /  j  k,  giving  the  perspective 
finishing  of  the  arches. 

Observe  the  dotted  lines  continued  from  I  m  n,  they 
show  how  each  arch  would  appear,  if  the  bridge  were 
transparent,  and  they  could  be  seen.  Unless  you  un- 
derstood the  true  drawing  of  the  whole  of  each  arch,  you 
could  not  draw  correctly  the  part  which  is  visible,  and  is 
represented  by  the  darker  line,  for  each  differs  from  the 
other,  and  to  draw  them  all  ahke  (as  is  frequently  done,  \ 
even  in  sketches  otherwise  correct,)  is  bad  perspective.  j 

Plate  12  represents  a  bridge  in  parallel  perspective, 
which  is  easier  than  oblique. 

The  exterior  arches  are  all  alike,  and  are  therefore 
drawn  without  the  aid  of  any  other  rule  than  that  of 
making  them  equal ;  lines  ruled  from  the  foot  of  each 
arch  to  the  point  of  sight,  give  the  direction  of  the  lines 
for  the  under  part  of  the  arch,  A  B  C  E.  These  lines 
are  at  right  angles  with  the  ground  line,  and  vanish  at 
5 


38 


LESSONS  IN  PERSPECTIVE. 


the  point  of  sight :  draw  a  hue  at  the  foot  of  the  bridge 
parallel  with  the  ground  line,  passing  through  the  foot 
of  each  arch  as  it  leaves  the  water  :  mark  on  this  line 
the  size  of  each  arch,  making  the  points  F  M  N  O, 
from  these  rule  lines  to  the  distance  point  D,  viz.  F  D, 
M  D,  N  D,  and  O  D,  cutting  the  base  line  of  the  arches 
at  P  Q  R  T.  This  gives  the  size  for  the  under  part  of 
each  arch,  and  also  for  the  end  T.  Draw  arches  like 
those  in  the  figure.  The  dotted  lines  show  the  true 
drawing  for  the  arches,  on  the  further  side,  (if  they 
could  be  seen.)  In  this  way,  you  get  the  true  appear- 
ance of  the  under  part  of  each  arch  of  a  bridge,  situate 
as  this  is,  with  regard  to  the  point  of  sight.  As  may  be 
seen  by  the  figure,  each  arch  differs  from  the  other  in 
the  drawing,  although  in  the  original  they  are  alike. 


LESSON  XII. 

INTERIORS. 

Interiors  are  drawn  in  perspective  by  the  rules 
already  given,  for  they  must  consist  of  lines  either 
parallel,  at  right  angles,  or  oblique  to  the  ground  line.* 

After  having  drawn  the  horizon  and  ground  lines,  and  ) 
points  of  sight  and  distance,  observe  what  lines  are  par- 
allel with  the  ground  hne,  and  draw  them  parallel,  their 
place  being  determined  by  their  distance  from  the 
ground  hne. 

Note  what  lines  are  at  right  angles  with  it,  whether 
they  are  on  the  walls  of  a  room  or  any  articles  of  fur- 
niture ;  the  vanishing  point  for  all  such  lines  is  the  point 
of  sight. 

*  Except  lines  inclined  to  the  ground  plane,  for  which  see  Les- 
son 14. 


LESSONS   IN  PERSPECTIVE. 


39 


If  any  objects  or  lines  are  oblique,  you  will  determine 
their  vanishing  points  on  the  horizon  line,  by  their  angle 
of  obliquity,  that  is,  by  the  angle  they  niake  with  the 
ground  line. 

To  illustrate  this,  see  Plate  13.  Make  the  requisite 
lines  and  points.  S  being  equal  to  S,  because 
you  need  a  distance  point  for  each  side.  In  parallel 
perspective,  you  may  set  off  the  distance  point  on  the 
horizon  line,  on  either  side  of  the  point  of  sight. 

Determine  the  size  of  the  room  by  a  scale,  or  your 
eye,  and  draw  the  boundary  lines  N  E  and  O  I.  Meas- 
ure the  length  of  the  sides  which  are  at  right  angles 
with  you,  and  lay  it  down  on  the  ground  line,  making 
E  F  for  one  side  and  I  J  for  the  other ;  draw  E  S  and 
I  S.  Draw  F  D^,  and  also  J  (not  drawn  in  the 
Plate.)  These  give  the  points  of  intersection  K  and  M, 
which  show  the  apparent  length  of  the  sides.  Draw 
N  S  and  O  S  for  the  top  lines  of  these  sides  ;  draw  the 
line  K  M  parallel  with  the  ground  line ;  raise  perpen- 
diculars from  the  points  K  and  M  till  they  strike  O  S  and 
N  S ;  draw  P  Q,  thus  you  get  the  back  wall  of  the 
room  P  Q  K  M. 

The  lines  for  the  top  and  bottom  of  the  windows, 
with  the  bars  which  are  parallel,  go  to  the  point  of  sight. 
The  dimensions  of  the  windows  are  marked  on  the 
ground  line.  R  T  for  the  first ;  U  I  for  the  second  : 
rule  lines  from  these  points  to  D^,  making  the  points  r  t 
u  V ;  at  these  raise  perpendiculars,  which  gives  the 
space  for  each  window,  u  v  being  the  smallest,  because 
it  is  the  most  distant ;  mark  the  length  of  the  windows 
on  the  boundary  line  of  the  side  N  E,  and  rule  the 
lines  X  S  and  y  S,  also  the  lines  for  the  window  bars, 
vanishing  at  the  point  of  sight.  Divide  the  space  R  T 
and  U  I  exactly  in  halves,  and  rule  to  D^  for  the  middle 
line  of  the  window  :*  smaller  divisions  are  made  in  the 

*  In  the  Plate  the  larger  window  only  has  the  middle  line. 


40 


LESSONS   IN  PERSPECTIVE. 


same  way,  but  are  not  drawn  on  this  figure,  lest  it  should 
be  confused.  The  same  rule  also  answers  for  pictures 
or  pannels,  on  the  walls  of  a  room. 

On  the  opposite  side  of  the  room  is  a  door.  Mark 
its  dimensions  and  place  on  the  ground  line  a  U,  and 
rule  to  D^,  mark  the  top  at  d,  and  rule  to  S,  getting 
efg  h  ;  this  is  the  door  frame.  The  door  stands  open. 
A  door  in  opening  describes  on  the  floor  an  arch  or 
portion  of  a  circle,  of  which  the  hinge  is  the  centre,  and 
the  bottom  of  the  door  a  radius  or  semidiameter.  Open 
a  door  quite  back  to  the  wall,  and  you  will  find  that  it 
describes  a  semicircle  ;  open  it  less,  and  the  bottom  of 
the  door  makes  an  angle  (more  or  less  large  according 
to  the  opening)  with  the  sill  of  the  door,  which  remains 
stationary  while  you  are  moving  the  door.  When  you 
have  ascertained  this  angle ;  in  other  words,  when  you 
have  opened  the  door  as  wide  as  you  wish,  you  have 
only  to  draw  the  door  in  your  sketch  at  the  same  angle, 
by  drawing  a  line  through  the  hinge  g  parallel  with  the 
ground  line,  and  letting  the  hne  for  the  door  make  with 
it  the  angle  required.  Produce  this  to  the  horizon  hne 
to  obtain  the  vanishing  point ;  thus  g  3  produced,  gives 
4  for  the  vanishing  point.  Draw  a  line  from  /  to  4  for 
the  top  ;  that  being  parallel  with  the  bottom,  must  have 
the  same  vanishing  point.  The  door,  now  it  is  open, 
is  no  longer  a  plane  at  right  angles  with  the  ground  line, 
as  it  would  be  if  shut,  and  as  the  wall  of  that  side  of 
the  room  is,  but  it  becomes  a  plane  standing  obHquely 
to  the  ground  line,  and  therefore  has  its  own  vanishing 
point,  viz.  4,  as  already  shown. 

In  order  to  obtain  accurately  the  point  3,  from  which 
the  perpendicular  3  9  is  raised  to  finish  the  outline  of 
the  door,  you  must  keep  in  mind,  that  the  door  in  open- 
ing, describes  a  semicircle,  ^  A  is  the  radius.  This 
circle,  or  a  quarter  of  it,  must  be  put  into  perspective^ 


LESSONS  IN  PERSPECTIVE. 


41 


which  is  very  easy,  since  this  is  only  to  put  a  square  in 
perspective. 

Lines  drawn  from  D^,  passing  through  the  points 
g  and  h  to  the  ground,  give  the  dimensions  of  the  radius  5 
they  are  identical  with  the  space  for  the  door,  viz.  the 
very  radius  in  question. 

Draw  a  line  from  U  to  S,  which  gives  one  side  of  the 
figure  in  which  the  quarter  circle  is  to  be  contained, 
while  g  h  already  drawn,  is  the  other.  The  figure  in 
which  a  quarter  of  a  circle  may  be  comprised,  is  a 
square,  one  fourth  less  than  the  square  by  which  the 
whole  circle  may  be  circumscribed:  see  Plate  10, 
where  each  circle  is  divided  into  four  squares. 
Having  drawn  the  line  U  S,  draw  a  line  through  h,  and 
another  through  g,  both  parallel  with  the  ground  line, 
and  intersecting  U  S  at  5  and  6.  The  square  is  then 
complete  6^5^.  Describe  within  it  the  quarter 
circle  from  h  to  5,  (which  you  can  do,  by  inspecting 
Plate  10,  figure  1,  without  making  any  more  lines,) 
and  where  the  line  for  the  bottom  of  the  door  strikes 
the  edge  of  the  circle,  as  at  3,  raise  the  perpendicular 
till  it  intersect  (at  9)  the  line  for  the  top  of  the  door. 

The  two  doors  in  the  back  side  of  the  room  are  also 
open.  Their  vanishing  points  are  found  as  in  the  door 
described  above ;  1  vanishes  at  7,  and  2  at  4. 


LESSON  XIII. 

TO  PUT  FURNITURE  AND  OTHER  SMALL  OBJECTS  FOUND 
IN  INTERIORS,  INTO  PERSPECTIVE. 

If  you  wish  to  put  furniture,  &c.  into  your  picture, 
this  also  must  be  drawn  according  to  the  rules  already 
given,  as  will  be  further  illustrated.    Keep  in  mind 
5* 


42 


LESSONS   IN  PERSPECTIVE, 


what  has  been  taught  with  regard  to  the  vanishing 
points  for  parallel  and  for  oblique  objects ;  and  remem- 
ber that  for  every  obhque  object,  whether  doors,  tables, 
chairs,  he,  you  must  have  distinct  vanishing  points, 
which  are  all  found  on  the  horizon  line,  except  in  cases 
where  the  planes  are  elevated  above,  or  depressed 
below^  the  parallel  of  the  ground  plane,  for  which  in- 
structions will  be  hereafter  given. 

You  must  first  determine  what  rule  the  object  you 
are  drawing  requires,  by  observing  vvhether  it  is  parallel 
or  oblique  ;  elevated  or  depressed.  When  this  is  done, 
the  difficulty  vanishes,  and  you  cannot  fail  in  applying 
the  rule,  if  you  have  become  famihar  with  its  use. 

Very  great  practice  is  necessary  to  insure  facihty. 
Accustom  yourself  to  regard  the  diflierent  aspects  or 
sides  of  objects  as  planes.  A  chair  for  instance,  may 
be  viewed  as  composed  of  planes,  perpendicular,  hori- 
zontal or  oblique.  The  floor  on  which  the  four  feet 
rest,  is  one  plane,  the  seat  is  another,  parallel  with  the 
former.  The  back  is  another  plane  at  right  angles 
with  the  seat,  or  perhaps  oblique  to  it.  The  four  sides 
reaching  from  the  seat  to  the  floor,  where  the  cross 
pieces  are  placed,  are  four  upright  planes,  at  right 
angles  with  each  other  :  for  if  the  chair  were  box^d  up 
from  the  floor  to  the  seat,  this  box  would  form  the  four 
planes  or  sides.  Thus  in  a  chair,  you  have  only  hori- 
zontal, perpendicular,  or  oblique  planes  to  put  into 
perspective,  which,  it  is  presumed,  you  can  now  do. 

It  may  be  well  to  mention,  that  in  oblique  perspective, 
the  distance  point  is  always  marked  on  the  prime  verti- 
cal line,  viz.  that  drawn  perpendicularly,  through  the 
point  of  sight ;  and  it  is  from  this  point  that  angles  are 
taken,  and  parallels  ruled  for  determining  the  vanishing 
points,  and  vanishing  lines  in  oblique  perspective. 

Plate  14  represents  several  articles  of  furniture  which 
afford  further  illustrations  of  the  rules  already  explained. 


LESSONS   IN  PERSPECTIVE,  4S 

The  chair  A  is  in  parallel  perspective,  and  the  lines 
vanish  at  S,  the  point  of  sight ;  as  will  be  seen  by  laying 
a  ruler  from  them  to  this  point.  The  boxes  B  and  C, 
and  also  the  footstool  E,  are  parallel.  The  chair  F  is 
oblique  :  vanishing  points  N  and  M.  It  will  be  found  that 
d  and  the  lines  parallel  with  it,  vanish  at  M,  and  that  A, 
and  its  parallels  vanish  at  N.  The  table  T  is  oblique, 
vanishing  points  V  and  W.  The  opening  of  the  hd  of 
the  box  C,  is  determined  on  the  same  principle  as  the 
opening  of  doors.  The  lid  in  opening  describes  the  arc 
of  a  circle,  of  which  e  a  is  the  radius,  the  hinge  being 
the  centre.  Put  this  circle  into  perspective  by  means 
of  a  square.  The  circle  being  put  into  perspective 
shows  w^here  to  draw  e  i,  which  must  terminate  at  the 
circumference.    Draw  /. 

If  you  did  not  understand  the  principle,  you  would 
be  likely  to  make  the  line  for  the  lid,  e  i  of  the  same 
length  as  e  a,  it  being  so  in  the  original ;  but  in  the  per- 
spective representation,  you  observe,  that  no  radius 
which  may  be  drawn  in  this  circle  is  of  the  exact  length 
of  e  a,  for  even  the  continuation  of  that  line,  as  e  n 
must  be  shorter  than  e  a,  because  that  half  of  the  circle 
is  farther  from  you,  than  the  half  in  which  the  radius 
e  a  lies,  and  consequently  must  appear  smaller. 

Neither  can  the  line  m  for  the  opening  of  the  other 
end  of  the  hd,  be  drawn  parallel  wath  i,  for  it  is  the 
corresponding  radius  to  e  i,  of  a  circle  nearer  than  the 
circle  e,  and  must  therefore  look  larger  than  that  :  m 
must  also  differ  from  r,  in  the  same  proportion,  and  for 
the  same  reason,  as  e  a  from  e  i. 

The  two  circles  or  rather  parts  of  circles,  are  given 
for  the  purpose  of  illustrating  the  importance  of  a  thor- 
ough knowledge  of  the  rules  of  perspective,  in  order  to 
draw  the  most  common  or  simple  object  with  truth. 

Having  once  understood  the  principle  on  which  an 
open  box  is  drawn,  you  will,  without  the  necessity  of 


44  LESSONS  IN  PERSPECTIVE. 

putting  circles  into  perspective,  be  able  to  draw  the 
parallel  sides  of  the  opening  with  correctness. 

You  will  observe  that  the  two  circles  partly  described 
on  the  plate,  for  the  purpose  of  determining  the  open- 
ing of  the  box,  are  circles  standing  upiight  on  the 
ground  plane,  and  not  laying  on  it,  as  are  the  circles  in 
Plate  10.  They  are  situate  like  picture  frames  on  the 
walls  of  a  room.  The  wheels  of  a  carriage  are  drawn 
in  the  same  way  ;  each  included  in  a  square,  put  into 
perspective,  according  to  its  position,  (whether  parallel 
or  oblique,)  and  its  distance  from  the  ground  line.  The 
spokes  are  so  many  radii,  not  one  of  which  you  could 
draw  correctly,  without  an  acquaintance  with  the  rules. 

As  you  have  learned  to  draw  squares,  whether  stand- 
ing upright  as  windows,  picture  frames,  &ic.,  or  lying 
on  the  ground  plane,  as  the  floor  of  a  house  :  (see  Plates 
8  and  9,)  you  will  have  no  difBculty  in  drawing  the 
squares  in  which  to  describe  your  circles,  whatever  may 
be  their  position.  After  having  gone  through  this  book, 
you  will,  it  is  presumed,  be  able  to  understand  more 
elaborate  works  on  perspective,  in  which  you  will  find 
a  greater  variety  of  cases. 

Another  method  of  obtaining  the  line  m,  for  the  second 
side  of  the  lid  of  the  box  C,  will  be  given  in  the  expla- 
nation of  Plate  16. 


LESSON  XIV. 

LINES  AND  PLANES  NOT  PARALLEL  WITH  THE 
GROUND  PLANE. 

Lines  and  planes  which  are  not  parallel  with  the 
ground  plane,  but  have  an  elevation  above,  or  depression 
below  it,  find  their  vanishing  points  above  or  below  the 


LESSONS  IN  PERSPECTIVE. 


45 


horizon  line,  determined  by  the  angle  of  their  elevation 
or  depression. 

A  book  lying  flat  on  a  table,  and  a  house  on  level 
ground,  are  parallel  with  the  ground  plane,  whether 
placed  obliquely  or  parallel  with  the  ground  line :  but 
houses  on  the  side  of  a  hill,  a  book  with  one  end  ele- 
vated, slanting  sides,  as  roofs  of  houses,  desks,  prisms, 
or  lines  laying  on  them  are  inclined  to  the  ground  plane, 
and  their  vanishing  points  are  found  on  the  vertical  line 
of  the  vanishing  point  of  their  base,  either  above  or 
below  the  horizon. 

The  directions  for  drawing  roofs  in  Lesson  9,  contain 
the  rules  required  for  the  drawing  of  planes  and  lines 
oblique  to  the  ground  plane  ;  but  it  is  thought  that  a 
further  illustration  of  the  subject  is  needful. 

In  Plate  1 5,  the  base  line  of  the  row  of  houses  A  makes 
an  angle  of  20°  with  the  ground  plane.  This  row  also 
stands  obliquely  to  the  ground  line,  and  the  angle  of  its 
obliquity  is  31*^.  This  angle  is  taken  from  the  distance 
point  D,  by  the  line  D  V  ;  V  is  the  vanishing  point  for  a 
line  laying  on  the  ground  plane,  and  inclined  to  the 
ground  line,  at  an  angle  of  31°.  Thus  if  the  row  of 
houses  A  stood  on  level  ground,  at  its  present  degree 
of  obhquity,  it  would  vanish  at  V.  Draw  the  radial  or 
vertical  line  of  the  vanishing  point  V,  which  is  (as  has 
been  shown  in  the  instructions  for  drawing  roofs)  a  per- 
pendicular line  drawn  through  this  point. 

Now  you  may  mark  on  this  radial,  from  V,  the 
degree  of  elevation  you  determine  on  for  the  houses,  as 
W  :  or  if  you  would  be  exact,  you  can  measure  it  by 
an  angle,  after  the  following  manner. 

Take  the  space  V  D  and  set  it  off  on  the  horizon  line 
from  V,  making  the  point  y  ;  this  is  the  radius  of  the 
vanishing  point  V.  From  ?/  as  a  centre,  make  the  true 
angle  of  elevation  which  the  row  has,  in  this  case 


46 


LESSONS  IN  PERSPECTIVE. 


20^*.  Where  it  strikes  the  radial  of  V,  viz.  at  W,  is 
the  vanishing  point  of  the  houses  A.  And  all  lines 
parallel  with  B  W,  as  the  roof,  windows,  and  the 
street,  vanish  at  W. 

You  will  seldom  find  it  necessary  to  take  angles. 
Draw  a  line  from  the  bottom  of  the  houses  to  the  hori- 
zon, at  the  degree  of  obliquity,  you  judge  right,  and 
then  make  a  point  as  W,  directly  over  the  vanishing 
point,  at  the  elevation  you  choose.  Make  all  parallel 
lines  vanish  at  W  ;  this  will  be  sufficient  for  the  common 
purposes  of  sketching. 

The  row  of  houses  C  is  in  parallel  perspective,  and 
stands  at  right  angles  with  the  ground  line,  therefore  the 
vanishing  point  is  on  the  prime  vertical  line.  The 
angle  of  its  elevation  is  20°.  The  distance  S  D  being 
laid  on  the  horizon  line  to  X,  the  angle  J  X  S  gives  J  for 
the  vanishing  point.  The  row  M  is  parallel,  and  has 
an  angle  of  depression  below  the  horizon.  The  distance 
S  D  transferred  to  the  horizon  hne  at  Z,  gives  the  angle 
S  Z  P.  P  is  the  vanishing  point  for  all  lines  parallel 
with  the  base  line  O  P. 

The  row  K  is  level  and  parallel,  and  vanishes  at  the 
point  of  sight. 

Plate  16,  figure  4  represents  an  inclined  plane.  A 
is  a  desk  standing  parallel.  The  drawer  or  base  is 
level,  and  the  side  a  vanishes  at  the  point  of  sight  S^. 
But  as  the  plane  A  is  elevated  at  an  angle  of  17°,  its 
vanishing  point  is  at  P,  and  the  sides  h  and  c  are  ruled 
to  P. 

If  you  wish  to  determine  the  size  of  the  desk  by 
measurement,  set  the  real  dimensions  of  the  side  a  on 
the  line  h  i,  and  from  h  rule  to  the  distance  point  D^. 

*  The  line  from  V  to  W  is  the  tangent  of  this  angle.  A  tangent 
is  a  line  drawn  from  the  point  where  a  radius  touches  the  circum- 
ference, at  right  angles  with  this  radius,  and  measures  the  angle^ 
W  V  is  the  tangent  of  the  angle  W  y  V. 


LESSONS  IN  PERSPECTIVE. 


47 


Where  this  intersects  at  d  is  the  apparent  size  of  this 
side,  because  it  is  parallel  with  the  ground  plane. 

But  in  order  to  measure  the  inclined  plane  A,  you 
must  take  another  distance  point,  because  you  have 
another  vanishing  point. 

Draw  a  horizontal  line  through  P,  (not  entirely  drawn 
in  the  figure,  to  prevent  confusion,  but  should  be  drawn 
by  the  pupil  in  copying  the  figure,)  which  will  be  the 
horizon  line  for  the  inclined  plane  A.  On  this  new 
horizon  set  your  distance,  viz.  the  space  from  P  to  D^, 
making  R.  PR  being  equal  to  P  D^.  R  is  the 
distance  or  measuring  point  for  all  lines  vanishing  at  P. 
Lay  a  rule  from  h  (the  true  measurement,  on  the  ground 
line  for  the  desk)  to  R,  it  intersects  at  T.  This  is  the 
apparent  size  of  the  desk  at  this  elevation,  and  which  if 
laid  flat  and  parallel  with  the  drawer,  would  be  of  just 
the  same  size  as  the  drawer  ;  for  the  space  from  P  to  R 
is  the  radius  of  the  vanishing  point  P,  set  off  on  its  own 
horizon.  Rule  the  line  T  r  parallel  with  i  n,  to  finish 
the  desk. 

Unless  you  have  a  perfect  acquaintance  with  these 
rules,  you  perceive  that  you  would  be  very  unlikely  to 
draw  the  desk  correctly,  even  if  it  were  before  your 
eyes.  Were  the  desk  a  little  more  or  less  open,  that  is, 
were  the  elevation  of  the  plane  A  a  little  more  or  less, 
the  line  T  r  could  not  be  drawn  as  it  is  now;  whereas, 
with  the  present  elevation,  if  it  were  not  drawn  precisely 
as  it  now  is,  it  would  not  belong  to  the  bottom  part  of 
the  desk.  The  measurement  h  n  is  the  same  for  the 
drawer  and  for  the  desk :  but  for  the  drawer,  the  dis- 
tance point  is  fixed  on  the  horizon  line  ;  and  for 
the  plane  A,  on  a  point  (R)  as  much  above  that,  as  P 
is  above  the  horizon. 

Plate  16,  figure  3  is  a  desk  elevated  at  an  angle  of 
15°,  and  placed  obliquely  to  the  ground  line.  V  and 
W  are  the  vanishing  points  for  the  two  sides  of  the 


48 


LESSONS  IN  PERSPECTIVE. 


part  which  stands  level.  X  is  the  vanishing  point  for 
the  sides  k  and  /,  which  are  elevated.  being  the 
point  of  sight  for  the  desk  figure  3.  above  it  is 
the  distance  point  on  the  prime  vertical  line,  whence 
angles  are  taken.  Make  V  u  equal  to  V  D^.  The 
radius  u  is  the  measuring  point  of  the  side  o  of  the 
desk,  which  is  level ;  and  the  point  above  it  Z,  the 
measuring  point  for  the  elevated  part  of  the  desk. 
Lines  1  2  3  are  parallel,  and  vanish  at  W  ;  4  5  are 
parallel,  and  vanish  at  V ;  and  k  and  I  are  parallel  and 
elevated  above  the  ground  plane,  and  vanish  atX;  lines 
from  Q  to  w  give  the  point  6,  and  from  Q  to  Z  the 
point  7. 

The  open  box  C,  Plate  14,  affords  an  example  of 
lines  depressed  below  the  ground  plane. 

After  one  side  of  the  lid,  as  e  i  is  found  by  means  of 
the  circle,  the  other  as  m,  may  be  ascertained  by  finding 
the  vanishing  point  of  the  first.  As  the  box  stands 
parallel,  this  must  be  on  the  prime  vertical  line  helow 
the  point  of  sight,  because  it  is  an  example  of  depres- 
sion, and  not  of  elevation. 

Produce  i  e  till  it  intersect  the  prime  vertical  line 
below  the  point  of  sight,  which  is  at  y,  and  this  is  the 
vanishing  point  required.  Rule  a  Hne  from  the  point 
y  through  the  edge  or  hinge  g,  till  it  intersect  the  line 
/,  and  it  will  give  the  line  m  with  the  same  exactness  as 
the  circle  does,  and  with  less  trouble. 

For  i  e  and  m  g  are  parallel  in  the  original,  therefore 
must  have  the  same  vanishing  point,  which  point  you 
ascertain  by  producing  i  e  to  the  prime  vertical  line  at  y. 

The  lid  of  the  box  is  a  plane  not  parallel  with  the 
ground  plane,  as  the  bottom  is,  nor  perpendicular  to  it, 
as  the  sides  are,  nor  parallel  with  the  perspective  plane, 
as  the  front  and  back  are  ;  but  it  is  inclined  to  the 
ground  plane,  and  also  to  the  perspective  plane,  having 
an  angle  of  depression  below  the  ground  plane. 


LESSONS  IN  PERSPECTIVE. 


49 


The  base  or  edge  of  this  inclined  plane,  (viz.  the 
line  e  at  which  it  touches  the  top  of  the  box,  where 
the  hinge  is,)  is  parallel  with  the  ground  plane,  and  the 
side  e  a  at  right  angles  with  the  ground  line  ;  therefore 
the  vanishing  point  for  the  inclined  lines  e  i  and  mg 
must  be  sought  on  the  prime  vertical  line,  that  being 
the  vanishing  line  for  all  planes  at  right  angles  with  the 
ground  line,  as  this  end  of  the  box  is. 

If  the  box  stood  obliquely  as  the  desk,  (in  Plate  16, 
figure  3,)  this  point  would  be  sought  on  the  radial  of 
the  vanishing  point  of  its  own  plane,  and  below  the 
horizon  line. 

If  you  have  any  doubt  whether  any  plane  (as  the  Hd 
of  the  box  C,  Plate  14)  is  depressed  below  or  elevated 
above  the  ground  plane,  and  therefore,  whether  its  van- 
ishing point  must  be  sought  above  or  below  the  horizon 
line,  you  have  only  to  observe  whether  the  bottom  or 
the  top  of  the  plane  is  farthest  from  you ;  if  the  top,  as 
the  upper  line  of  the  roof  of  a  house,  or  of  a  desk  (like 
T  r  and  1  7,  figures  3  and  4,  Plate  16)  recedes,  then  the 
vanishing  point  is  above  the  horizon,  for  it  is  the  re- 
ceding part  which  looks  smallest,  and  the  fines  of 
course  converge  to  produce  this  diminution.  But  if  the 
bottom  is  the  receding  part,  (as  the  line  e  ^  in  the  box 
C,  Plate  14,)  then  the  vanishing  point  is  below  the 
horizon. 


LESSON  XV. 

COLONADES  AND  STEPS. 

Plate  16,  figure  1  represents  a  colonade  or  row  of  pil- 
lars, on  each  side  the  point  of  sight,  that  is,  on  the  right 
and  left  of  the  spectator.   The  lines  which  vanish  go  to  the 
point  of  sight,  therefore,  it  is  parallel  perspective.    It  is 
6 


60 


LESSONS   IN  PERSPECTIVE. 


thought  that  this  figure,  and  an  inspection  of  Plate  11, 
where  the  arches  of  a  bridge,  in  obhque  perspective, 
are  exhibited,  will  be  sufficient  to  enable  the  pupil  to 
apply  the  rules  to  colonades  and  arches  in  oblique  per- 
spective. The  divisions  are  made,  and  the  measure- 
ments taken  for  a  colonade  viewed  obliquely,  in  the 
same  manner  as  for  a  bridge  or  a  single  arch  of  a  bridge 
viewed  obliquely. 

The  columns  appear  shorter  and  narrower  as  they 
approach  the  vanishing  points. 

The  floor  in  figure  I  is  divided  into  squares  to  rep- 
resent the  figure  of  a  carpet,  or  a  pavement,  after  the 
following  manner.  Draw  hnes  from  the  divisions  on  the 
ground  line  to  S,  the  point  of  sight.  Draw  the  diagonal 
E  D  from  the  first  square  to  the  distance  point.  This 
diagonal  intersects  each  line,  showing  the  size  of  each 
row  of  squares.  Draw  parallel  lines  through  the  points 
of  intersection.  By  this  process,  you  find  (as  appears 
by  figure  1,  Plate  16)  the  exact  proportion  in  which 
each  square  diminishes  as  it  recedes  from  the  eye.  It 
will  be  easy  to  draw  any  figure  (a  circle  for  instance) 
within  the  square,  as  is  done  in  two  of  the  nearest 
squares  on  the  figure.  The  diagonals  of  each  square 
will  give  the  centre,  through  which  centre  rule  a  line 
for  the  diameter.  If  it  is  parallel  perspective,  the  line 
for  the  diameter  is  parallel  with  the  ground  line  ;  if 
oblique,  it  goes  to  its  vanishing  point. 

This  diameter  will  show  how  much  larger  the  nearer 
half  of  the  square  appears,  than  the  more  remote.  If 
the  figures  are  of  an  oval  shape,  you  must  put  parallel- 
ograms into  perspective,  instead  of  squares,  which  you 
can  easily  accomplish  by  observing  Plates  8  and  9,  or 
by  the  help  of  a  ground  plan. 

Figure  2,  Plate  1 6,  shows  the  manner  of  drawing 
steps  in  perspective.  E  two  steps  parallel,  F  two  ob- 
lique.   It  is  in  fact  only  putting  so  many  boxes,  or 


LESSONS   IN  PERSPECTIVE. 


solid  rectangular  objects  placed  one  on  top  of  another 
in  perspective.  You  could  easily  draw  one  box  as  c, 
in  true  perspective,  and  why  not  another  as  A,  imntiedi- 
ately  below  it  ?  The  parts  E  and  a  correspond  with 
the  tops  of  the  boxes,  as  they  appear  seen  below  the 
horizon  :  see  also  the  box  B,  Plate  14.  If  they  were 
above  the  horizon,  you  could  not  seethe  tops.  By  this 
rule,  in  looking  at  an  object,  you  may  ascertain  at  once, 
whether  any  part  of  it  is  above  the  horizon,  that  is, 
above  the  height  of  your  eye.  When  you  are  on  level 
ground,  you  cannot  see  over  the  top  of  a  house ;  but 
when  you  are  on  a  high  hill,  you  can  see  over  the  tops 
of  the  houses  on  the  plain  below.  If  you  are  in  a  room 
you  cannot  see  the  top  of  a  piece  of  furniture  which  is 
higher  than  your  head,  while  those  articles  which  are 
lower  than  your  eye,  as  a  table,  show  their  upper  sur- 
faces, occupying  more  or  less  space,  (viz.  looking  wider 
or  narrower)  as  they  are  nearer  to  or  farther  above  the 
floor.  Therefore,  if  in  a  view,  the  tops  of  houses  are 
drawn,  the  horizon  must  be  a  high  one,  for  it  would  be 
apparent  to  any  one  acquainted  with  perspective,  that 
your  sketch  was  taken  from  a  height. 

The  steps  F,  Plate  6,  figure  3,  are,  as  it  regards  their 
drawing,  two  boxes,  one  on  the  other,  placed  obliquely, 
and  having  their  vanishing  points  on  the  horizon  line  at 
and  W2. 


That  the  rules  given  in  these  lessons  will  give  the 
true  perspective  drawing  of  objects,  may  be  experimen- 
tally proved  by  the  following  method.  Provide  a  large 
table  ;  this  is  a  horizontal  plane,  and  will  represent  the 
ground  plane,  viz.  the  earth,  on  which  objects  are  situate. 
Station  at  the  edge  of  one  side  of  this  table,  a  little  figure 
to  represent  the  spectator,  or  person  taking  the  view.  A 


52 


LESSONS  IN  PERSPECTIVE, 


Stick  of  four  or  six  inches  in  height,  with  a  hole  in  the 
top  for  the  eye,  vAW  answer  the  purpose,  it  must  be 
securely  fastened  to  the  table. 

At  a  suitable  distance  from  the  spectator,  (say  two  or 
three  times,  the  height  of  the  figure)  set  up  a  frame  like 
a  picture  frame  without  a  glass,  at  right  angles  with  the 
table,  that  is,  standing  upright  upon  it.  This  is  to  rep- 
resent the  perspective  plane.  Put  a  line  across  the  per- 
spective plane  horizontally,  at  the  same  height  as  the  eye 
in  your  figure.  This  line  represents  the  horizon. 
The  best  way  to  fasten  this  line  is  to  attach  a  small 
weight  to  each  end  of  it,  insert  pins  into  the  frame  at 
the  proper  height,  and  lay  the  line  across.  The  weight 
hanging  down  over  the  pins  will  keep  the  cord  tight. 
If  you  wish  a  higher  or  lower  horizon,  elevate  or  shorten 
the  figure,  and  alter  the  pins  and  line  accordingly  ; 
always  remembering  that  the  line  must  be  at  the  same 
distance  from  the  table  or  ground  plane  as  the  eye. 

Mark  the  point  in  this  horizon  line  directly  opposite 
the  eye,  whether  it  be  the  centre  of  the  frame,  or 
nearer  to  one  side  than  the  other.  This  is  the  point  of 
sight.  It  is  convenient  to  be  able  to  move  the  figure  to 
the  right  or  left,  as  this  changes  the  point  of  sight,  and 
enables  you  to  vary  your  experiments. 

Through  this  point  of  sight  pass  another  cord  perpen- 
dicularly, and  fasten  it.  This  is  the  prime  vertical  line, 
passing  through  the  point  of  sight.  Plate  14,  H  W  the 
horizon  line,  and  D  S  ^  the  prime  vertical  line,  repre- 
sent the  two  lines  here  described.  Prepare  a  model  of 
a  house,  box,  bridge,  or  any  object,  the  true  drawing  of 
which  you  wish  to  ascertain  ;  place  it  behind  the  4)er- 
spective  plane,  to  the  right  or  left  of  the  point  of 
sight,  and  at  any  distance  you  choose. 

Attach  threads  to  the  corners,  and  to  the  top  and 
bottom  of  the  sides  next  the  perspective  plane,  which 


LKSSONS   IN  PERSPECTIVE. 


53 


are  the  only  parts  that  can  be  seen  ;  bring  all  these 
threads  through  the  perspective  plane,  converging  to 
the  eye  of  the  figure,  and  fasten  them  securely  at  the 
back.  These  represent  rays  of  light  in  their  passage 
from  the  object  to  the  eye. 

It  will  appear  that  the  points  at  which  the  threads 
enter  the  perspective  plane,  in  coming  to  the  eye,  give 
the  same  drawing  which  the  measurements,  points  and 
angles  do,  in  a  drawing  from  a  ground  plan  :  provided 
the  proportions,  size,  distances,  &ic.  correspond. 

If  you  look  through  the  hole  designed  for  the  eye,  at 
the  same  time  placing  a  pencil  or  small  rod  on  the  per- 
spective plane,  so  as  to  conceal  the  lines  in  the  original 
object  from  the  eye,  you  will  find  that  it  strikes  just 
where  the  threads  enter  the  perspective  plane. 

Lay  a  ground  plan  of  a  floor  of  a  house,  or  of  circles, 
like  those  in  Plates  8,  9,  and  10,  on  a  table,  behind  the 
perspective  plane,  so  as  to  have  this  plane  between  the 
eye  and  the  ground  plan.  Substitute  for  the  vacant 
frame,  one  with  a  plate  of  glass  in  it,  as  a  perspective 
plane  ;  you  can  trace  with  a  pencil  on  this  glass,  or 
measure  with  compasses,  the  appearance  of  the  figures 
beyond.  By  placing  your  eye  in  the  hole  for  the  eye 
of  the  figure,  you  will  see  that  the  drawing  is  the  same 
as  that  resulting  from  the  measurements,  angles,  he* 
already  given  in  the  rules  of  perspective,  the  proportion 
and  distances  being  preserved. 

Objects  may  be  placed  in  any  position,  and  be  of 
any  shape,  and  their  true  perspective  dehneation  can  be 
ascertained  by  attaching  threads  to  their  outline  or 
edges,  and  bringing  them  to  the  eye,  after  the  manner 
detailed  in  the  above  description. — The  proportions 
must  be  exactly  preserved. 

Your  figure  or  spectator,  which  is  presumed  to  be 
about  six  feet  high,  affords  a  good  scale,    A  complete 
6* 


54 


LESSONS   IN  PERSPECTIVE, 


model  of  a  person  taking  a  sketch,  with  all  the  objects 
in  their  true  situation  may  thus  be  made.  The  threads 
attached  to  each,  and  carried  to  the  eye,  will  show  the 
angles  under  which  every  object  is  seen,  and  thus  de- 
termine the  true  drawing. 

The  diminishing  of  figures  in  a  landscape  according 
to  their  distance  from  the  ground  line,  may  be  experi- 
mentally proved,  by  fastening  one  thread  to  the  head, 
and  another  to  the  foot  of  each  of  the  figures,  placed  at 
different  distances  on  the  ground  plane.  It  will  then 
appear  how  much  smaller  the  angle  is  (viz.  how  much 
nearer  the  threads  approach  each  other  in  passing  to 
the  eye)  when  the  figure  is  far  off,  than  when  it  is 
near.  A  figure  of  a  man  placed  at  six  inches  from  the 
ground  line,  will  in  this  experiment,  be  seen  under  a 
much  larger  angle  than  a  similar  figure  twelve  or  twenty 
inches  distant. 

It  will  also  appear  that  such  figures  never  rise 
above  the  horizon  line,  unless  they  are  on  elevated 
ground.  If  the  spectator  is  sitting  on  the  level  of  the 
ground  plane,  a  figure  standing  up  will  rise  above  the 
horizon,  or  if  the  spectator  is  on  a  hill  or  the  top  of  a 
building,  the  figure  will  appear  below  his  horizon. 

It  is  evident  that  if  a  plane  were  extended  horizontally 
from  the  eye  to  the  verge  of  the  horizon,  every  object 
on  the  ground  plane,  not  higher  than  the  eye,  would  be 
under  this  horizontal  plane. 


LESSON  XVI. 

RECAPITULATION. 

The  rules  of  perspective  are  not  numerous  or  diffi- 
cult to  comprehend,  but  as  they  include  ideas  which 
are  abstract,  they  should  be  practically  applied  to  a 
variety  of  cases,  by  a  course  of  drawing  in  perspective. 


LESSONS  IN  PERSPECTIVE. 


The  pupil  having  once  made  himself  familiar  with 
the  principles  which  these  rules  involve,  will  find  no 
difficulty  in  sketching  with  truth  and  expression,  any 
object  within  his  sight,  without  having  recourse  to  many 
of  the  elaborate  methods  described  in  this  book.  Let 
him  not  expect,  however,  to  arrive  at  this  facility,  by 
any  more  expeditious  course  than  that  of  copying  the 
figures  in  the  plates,  and  making  practical  applications 
of  the  rules  here  given. 

To  such  it  is  believed,  that  the  following  brief  enu- 
meration of  the  rules  and  principles  of  perspective  may 
be  acceptable  ;  although  they  may  be  scarcely  intelh- 
gible  to  those  who  have  no  previous  acquaintance  with 
the  subject. 

1.  Objects  are  seen  by  means  of  rays  of  light,  pro- 
ceeding from  them  in  straight  lines,  and  converging  and 
entering  the  pupil  of  the  eye. 

2.  These  rays  form  a  cone  whose  apex  is  the  eye. 

3.  The  true  drawing  of  objects  is  at  the  points 
where  these  rays  would  intersect  a  perpendicular  trans- 
parent plane,  if  such  were  interposed  between  them 
and  the  spectator. 

4.  The  object,  the  rays  of  light,  and  the  eye,  form 
a  triangle  or  cone,  whose  base  is  the  object.  The 
size  of  this  angle  is  determined  by  the  size  of  the 
object,  and  its  distance  from  the  beholder.  When 
similar  angles  are  made  on  a  flat  surface,  a  true  linear 
representation  is  obtained ;  this  is  what  perspective 
teaches. 

5.  The  distance  point  represents  the  distance  of  the 
eye  from  the  perspective  plane.  Lines  drawn  to  it, 
from  dimensions  laid  down  on  the  ground  line,  form 


56 


LESSONS   IN  PERSPECTIVE. 


the  same  angle  as  is  made  by  the  rays  of  light  in  the 
original. 

6.  Lines  parallel  with  the  ground  line  in  the  original, 
are  drawn  parallel :  They  have  no  vanishing  point. 

7.  Original  lines  which  are  parallel,  if  they  vanish, 
have  the  same  vanishing  point. 

8.  Original  lines  at  right  angles  with  the  ground 
line,  have  iheir  vanishing  point  in  the  point  of  sight. 

9.  Original  lines  oblique  to  the  ground  line,  have 
their  own  vanishing  and  distance  points. 

10.  These  points  are  ascertained  by  means  of  par- 
allels drawn  from  the  point  of  distance  on  the  prime 
vertical  line  to  the  horizon.  The  intersection  of  these 
parallels  with  the  horizon  gives  the  vanishing  points, 
and  the  radii  of  these  vanishing  points,  transferred  to 
the  horizon  line,  give  the  distance  points,  or  as  they  are 
also  called,  the  measuring  points. 

11.  Circles  and  arches  are  drawn  by  means  of 
squares,  sines  and  cosines  put  into  perspective,  by  the 
foregoing  rules. 

12.  Planes  and  lines  on  them,  which  are  inclined 
to  the  ground  plane,  find  their  vanishing  points  on  the 
radial  of  their  own  vanishing  plane.  The  place  for  these 
vanishing  points  is  determined  by  the  angle  of  their 
inclination,  and  their  measuring  points,  are  found  by 
the  radii  of  their  own  vanishing  points,  and  have  the 
same  level  above  or  below  the  horizon  as  these  vanish- 
ing points. 


LESSONS  IN  PERSPECTIVE. 


57 


LESSON  XVII. 

SHADOWS. 

Every  one  has  observed  that  the  higher  up  the  sun 
gets,  the  shorter  the  shadows  of  objects  become.  This 
fact  teaches,  that  in  making  the  shadows  of  a  picture, 
regard  must  be  had  to  the  position  of  the  hght,  which 
must  be  the  same  for  every  object  in  the  same  picture. 
You  must  not  therefore  put  into  your  view  a  figure 
with  a  long  shadow,  as  if  the  sun  were  not  more  than 
an  hour  high,  and  a  tree  or  a  house  with  a  shadow  no 
longer  than  it  would  cast,  with  the  sun  at  three  or  four 
hour's  height. 

As  light  comes  to  us  in  straight  lines,  it  is  evident, 
that  when  any  opaque  object  is  in  the  way,  it  will  inter- 
sect such  rays  as  meet  it  in  their  progress.  And  there 
will  be  a  space  beyond  the  opaque  object,  which  will 
receive  no  light  from  the  luminous  body,  although  it 
may  receive  some  reflected  light  from  surrounding 
objects,  which  will  lesson  the  darkness  of  the  shadow. 
This  space  of  shade  will  bear  a  definite  relation  to  the 
shape  of  the  object ;  but  it  will  not  always  assume  pre- 
cisely the  same  shape,  because  the  shadow  may  be 
longer  or  shorter,  according  to  the  height  of  the  light, 
and  broader  or  narrower,  according  to  the  position  of 
the  beholder. 

The  first  thing  then  to  be  attended  to  in  projecting 
shadows,  is  the  position  of  the  light. 

If  the  luminous  body  is  larger  than  the  opaque,  the 
shadow  will  diminish  as  it  recedes  from  the  opaque 
body  which  casts  it ;  but  if  the  opaque  body  is  larger, 
then  the  shadow  will  increase  in  width  as  it  recedes. 

There  are  three  different  positions  of  the  sun  to  be 
attended  to  in  sketching  from  nature.    1st,  When  it  is 


58 


LESSONS   IN  PERSPECTIVE. 


before  the  perspective  plane  or  picture  ;  2d,  when  it  is 
behind,  and  3d,  when  it  is  in  the  plane  of  the  picture. 

If  you  imagine  a  window  or  perspective  plane  before 
you,  on  which  the  objects  beyond  may  be  drawn,  and 
the  sun  is  beyond  the  window  and  the  objects,  so  that 
its  light  strikes  on  that  side  of  them  which  you  do  not 
see,  then  the  light  is  said  to  be  behind  the  picture,  and 
the  shadows  will  be  thrown  towards  you,  and  will  appear 
larger  than  when  cast  from  you. 

2d,  If  the  sun  is  behind  you,  and  strikes  on  that  side 
of  objects  which  you  see,  and  the  spectator  is  situate 
between  the  sun  and  the  perspective  plane,  then  the 
sun  is  said  to  be  before  the  picture,  and  you  will  see 
less  of  the  shadow,  which  will  be  cast  from  you,  than  if 
the  sun  were  behind  the  picture. 

3d,  If  the  sun  is  on  a  line  with  the  perspective  plane  ; 
that  is,  so  placed,  that  were  the  perspective  plane  ex- 
tended till  it  reached  the  sun,  it  would  go  neither  before 
nor  behind,  but  just  through  it,  then  the  sun  is  in  the 
same  plane  as  the  picture,  and  the  shadows  fall  in  a 
line  parallel  with  the  ground  line. 

The  general  remarks  already  made,  may  be  sufficient 
for  the  common  purposes  of  sketching ;  but  further 
illustrations  of  the  subject  are  given,  for  the  use  of  such 
as  desire  to  be  accurate  in  the  forms  of  their  shadows. 
To  understand  these  illustrations  requires  some  study 
and  attention  ;  they  are  however  rendered  as  clear  and 
simple  as  the  subject  permits. 

To  obtain  the  precise  shadow  cast  by  a  given  opaque 
object,  first  determine  the  position  of  the  sun,  whether 
it  is  before,  behind,  or  in  the  same  plane  as  the  picture, 
and  also  its  height,  or  altitude,  as  it  is  technically  called. 

In  order  to  do  this,  draw  a  ground  line,  horizon  line, 
point  of  sight,  and  prime  vertical  line,  and  the  object 
whose  shadow  is  required,  which  object  must  be  drawn 
in  true  perspective. 


LESSONS   IN  PERSPECTIVE. 


59 


The  sun  appears  to  be  over  some  point  of  the  horizon, 
either  on  your  right  hand  or  your  left.  You  can  select 
this  point  according  to  your  judgment,  but  if  you  wish 
any  particular  place,  as  40^  from  the  point  of  sight, 
make  an  angle  of  40°  (Plate  17)  from  D,  the  distance 
point  on  the  prime  vertical  line,  obtaining  the  point  C. 
This  is  called  the  angle  of  the  sun's  declination,  through 
this  point,  C,  rule  a  perpendicular,  the  sun's  place  is 
somewhere  on  this  perpendicular.  You  can  fix  on  any 
height,  but  if  you  wish  to  do  it  with  exactness,  take  the 
radius,  that  is,  the  distance  C  D,*  and  set  it  off  on  the 
horizon  line  from  C,  making  the  point  E.  From  E 
make  the  angle  of  the  sun's  altitude,  (in  this  case  30°,) 
and  the  point  where  this  angle  intersects  the  sun's  per- 
pendicular, as  at  F,  is  the  height  of  the  sun.  Thus  you 
can  determine  with  precision  any  given  altitude,  and 
position  of  the  sun,  by  means  of  angles  from  the  distance 
and  radius  points. 

Having  fixed  on  the  point  for  the  light,  if  you  wish  to 
find  the  exact  shadow  of  any  given  object,  as  K,  regard 
must  be  had  to  the  perpendicular  lines,  or  sides  of  the 
object,  as  a  6  c.  C  is  a  point  on  the  horizon  line,  per- 
pendicularly under  the  sun,  called  the  seat  of  the  light. 
Draw  a  straight  line  from  C  through  the  bottom  of  the 
side  a,  and  another  straight  line  from  F  the  sun  him- 
self, through  the  top  of  the  side  a.  They  intersect  each 
other  at  d,  and  thus  determine  this  point.  Then  draw 
a  line  from  C,  passing  through  the  bottom  of  the  side  b, 
and  one  from  F,  through  the  top,  they  cross  at  c,  which 
gives  this  point.  Then  take  the  bottom  and  top  of  the 
side  c,  after  the  same  manner,  which  gives  g,  and  join- 

*  It  cannot  be  made  too  familiar  to  the  pupil,  that  the  radius  of 
any  point,  is  the  distance  of  that  point,  (as  C,)  from  the  distance 
point,  (as  D  on  the  prime  vertical  line,)  set  off  from  the  vanishing 
point  on  the  horizon  line,  as  C  E  Plate  17. 


60 


LESSONS  IN  PERSPECTIVE. 


ing  these  points,  viz.  d  e  the  whole  figure  of  the 
shadow  is  determined. 

Now  if  the  sun  were  situate  lower,  that  is,  nearer  the 
horizon,  as  at  L,  the  lines  from  C  through  the  base  of 
the  perpendiculars  ah  c  must  be  produced,  and  lines 
from  L,  the  sun's  place,  drawn  through  the  tops,  making 
h  i  j.  Observe  how  much  farther  the  shadow  extends 
when  the  sun  is  low,  and  also  that  the  shape  is  differ- 
ent. This  plainly  illustrates  the  necessity  of  fixing  a 
height  for  the  light  in  all  pictures,  into  which  shadows 
are  introduced.  Mathematical  exactness  may  not  al- 
ways be  required,  but  without  a  knowledge  of  these 
principles,  you  might  be  liable  to  incongruities. 

In  this  example,  the  sun  is  behind  the  picture,  and 
the  shadows  fall  towards  the  spectator. 

If  the  sun  is  before  the  picture,  continue  the  perpen- 
dicular from  C,  (the  sun's  seat  in  the  horizon,)  below 
the  horizon  line.  Let  M  be  the  sun,  (figure  2,  Plate 
17,)  C  his  seat  on  the  horizon  line.  Draw  lines  through 
the  top  and  bottom  of  the  perpendicular  sides  of  the 
solid  P,  as  before.  Those  from  C  to  the  bottom,  and 
those  from  M  to  the  top.  The  lines  from  the  light 
itself  always  go  to  the  top,  and  those  from  the  seat  of  the 
light,  to  the  bottom  of  all  perpendiculars  of  which  you 
seek  the  shadows,  C  m  for  the  base  m  of  this  side,  and 
M  n  for  the  top  intersecting  at  O.  You  must  also 
ascertain  the  shadow  of  the  side  not  seen,  (but  which 
is  drawn  in  dotted  lines.)  The  lines  for  this  side  inter- 
sect at^.     Join  p  0,  the  shadow  is  then  complete. 

If  the  sun  is  lower  than  at  M,  mark  its  place  nearer 
the  horizon  line,  as  at  R  :  if  higher,  farther  from  the 
horizon  line.  The  shadow  is  obtained  correctly  by 
this  mode,  because  the  lines  or  angles  drawn,  are  the 
same  which  the  rays  of  light  proceedin-g  from  the  sun, 
at  the  given  height  and  position,  and  arrested  by  the 
given  object,  would  make ;  and  all  rays  within  the  two 


LESSONS  IN  PERSPECTIVE* 


BXterior  ones  drawn  in  the  figure,  are  intercepted,  and 
do  not  reach  the  ground. 

When  the  sun's  place  is  beyond  the  picture,  it  is 
truly  represented  by  a  point  above  the  horizon  line  ;  and 
when  it  is  before  the  picture  by  a  point  on  the  other 
side,  that  is,  below  the  horizon  line. 

3d,  When  the  sun  is  in  the  plane  of  the  picture, 
Plate  18,  figure  1,  draw  horizontal  lines  through  the 
base  of  the  object,  as  a  b  and  c  d.  Intersect  them  by 
lines  touching  the  top,  and  making  the  same  angle  with 
the  horizon,  as  the  angle  of  the  sun's  elevation.  The 
dotted  line  b  gives  a  less  elevation  than  the  dark  lines, 
consequently  a  longer  shadow. 

The  opaque  object  A  (figure  1,  Plate  18)  is  oblique 
both  to  the  horizon  and  the  ground  plane.  Draw  hori- 
zontal lines  from  the  base  of  its  perpendicular  sides  i 
and  /,  intersected  by  lines  through  the  tops  of  these 
sides,  drawn  at  the  angle  of  the  sun's  elevation.  This 
gives  the  points  g  h;  from  g  draw  a  line  to  the  lowest 
point  in  the  object  e,  and  you  have  the  shadow.  For 
the  shadow  of  every  other  perpendicular  line  in  the 
object  taken  in  the  same  way,  would  fall  within  this 
figure. 


LESSON  xvm. 

SHADOWS.  CONTINUED. 

If  the  light  proceed  from  a  lamp  or  other  luminous 
body  on  the  earth,  situate  in  a  room  or  out  of  doors,  it 
must  be  perpendicularly  over  some  place  in  the  ground 
plane.  This  is  called  its  seat ;  whereas  the  seat  of  the 
sun's  light  by  reason  of  his  immense  distance,  is  always 
supposed  to  be  on  the  horizon  line. 

Mark  this  point  (Plate  18,  figure  2,  C)  on  the  ground 
7 


62 


LESSONS   IN  PERSPECTIVE. 


plane  of  your  picture,  viz.  the  floor  or  earth  on  which 
objects  stand.  Rule  a  perpendicular  through  it,  and 
mark  the  height  of  the  light  on  this  perpendicular. 

Draw  lines  from  the  seat  of  the  light  C,  on  the  ground 
plane,  through  the  foot  of  the  object,  as  the  lines  m  n  o 
on  the  solid  o  ;  and  lines  from  the  light  through  the  top 
P  r  S.  The  points  of  their  intersection  t  u  mark  the 
extent  of  the  shadow.  The  only  difference  between 
this  light  and  the  light  of  the  sun,  is,  that  the  sun  is 
always  supposed  to  have  its  seat  on  the  horizon  line  ; 
but  when  the  light  is  stationed  on  the  earth,  its  seat  is 
on  the  ground  plane.  In  both  cases,  the  seat  is  always 
perpendicularly  under  the  luminous  body.  In  the  case 
of  the  sun's  being  before  the  picture,  his  position  is 
marked  below  the  horizon,  as  figure  2,  (Plate  17.) 
This  method  is  resorted  to,  because  all  the  hnes  are 
drawn  on  a  flat  surface,  as  a  sheet  of  paper ;  but  the 
sun  is  nevertheless  supposed  to  be  above  the  horizon 
line,  although  on  the  nearer  side  of  it. 

Thus  in  projecting  shadows,  you  have  only  to  mark  two 
points,  the  one  perpendicularly  over  the  other,  viz.  the 
seat  of  the  light,  either  on  the  horizon  or  ground  plane, 
and  its  height.  From  these  points,  rule  straight  lines 
to  the  top  and  bottom  of  every  side  of  the  object,  re- 
membering that  those  to  the  top  of  the  object,  must 
always  proceed  from  the  luminous  body  ;  those  through 
the  bottom,  from  its  seat."^ 

If  the  object  which  casts  the  shadow  is  oblique,  as  B, 
figure  2,  (Plate  18,)  rule  a  horizontal  line  M  through 
the  seat  of  the  light,  and  a  line  from  the  height  of  the 
light  N,  passing  through  the  top  of  the  oblique  object. 
W,  the  point  where  these  lines  intersect,  is  the  extent 

*  Unless  the  light  be  below  the  object,  as  when  it  is  suspended  in 
the  air,  or  a  room,  and  strikes  the  under  part  of  the  object,  in  which 
case,  lines  from  the  light  go  to  the  bottom,  and  from  its  seat,  to  the 
top  of  the  object. 


LESSONS   IN  PERSPECTIVE. 


of  the  shadow.  From  this  point,  draw  a  straight  line 
to  its  extreme  base,  or  lowest  point,  and  this  gives  the 
exact  form  of  the  shadow,  as  W  X. 

Shadows  take  the  form  of  the  objects  on  which  they 
fall ;  thus  the  shadow  of  a  line  on  a  circular  object  will 
be  curved. 

If  shadows  are  intercepted  by  objects,  draw  them 
first,  as  if  nothing  were  in  the  way,  and  then  raise  per- 
pendiculars from  the  points  of  interception  to  the  top  of 
the  intercepting  object,  and  continue  the  shadow  across. 

The  reflection  of  objects  from  the  water  is  an  exact 
image  of  the  object  reversed. 

Draw  this  image  reversed  from  the  foot  of  the  object, 
and  of  the  same  dimensions,  and  that  part  which  ex- 
tends over  the  water,  will  be  the  part  reflected.  (See 
Plate  18,  figure  3  ;  2  being  farther  from  the  water  than 
either  4  or  1.) 


64 


LESSONS   IN  PERSPECTIVE. 


CONCLUSION. 


Many  more  illustrations  of  the  rules  of  perspective 
might  be  given,  which  would  be  useful  to  the  learner, 
but  they  would  too  much  increase  the  size  of  this  vol- 
ume. It  is  hoped  that  any  one,  after  a  faithful  study  of 
what  is  here  explained,  may  be  able  to  understand  more 
scientific  treatises,  and  obtain  from  them  any  additional 
know^ledge  he  may  require.  A  few  hints  are  added 
as  to  the  finishing  up  of  sketches. 

Linear  perspective,  which  regards  the  drawing  and 
outline  of  objects,  is  scarcely  more  important  than  ariel 
perspective,  or  their  tinting  and  shading.  An  object 
must  be  drawn  smaller  and  coloured  fainter,  in  propor- 
tion to  its  distance.  The  lights  should  be  less  bright, 
and  the  shadows  less  strong,  as  they  recede  from  the 
foreground. 

The  observation  and  study  of  nature,  is  the  best  guide 
for  the  composition  of  light  and  shade  in  a  picture. 
Beautiful  effects  of  light  and  dispositions  of  shadow,  may 
at  times  be  seen  to  lend  a  new  and  indescribable  charm 
to  the  landscape.  These  should,  if  possible,  be  secured 
as  soon  as  they  are  observed,  by  sketching  the  scene, 
and  putting  it  in  the  same  light  and  shade. 

It  is  also  of  advantage  to  consult  fine  engravings  and 
paintings,  and  when  a  happy  composition  occurs  in  any 
of  these,  imitate  it  in  one  of  your  own  sketches  as 
nearly  as  the  difference  of  the  subjects  will  permit. 


LESSONS  IN  PERSPECTIVE. 


65 


Let  the  shadows  be  broad  and  in  masses,  and  the 
lights  sparing,  and  not  scattered  indiscriminately.  The 
most  common  fault  with  beginners,  is  to  have  too  many 
hghts,  and  these  equally  bright.  The  brightness  of  a 
light  depends  on  the  depth  of  the  shade  with  which  it 
is  contrasted.  White  paper  in  the  distance,  shaded  by 
a  faint  tint,  will  look  remote,  but  the  same  white  in  the 
foreground,  opposed  to  very  dark  touches,  will  be  bril- 
liant and  near.  Aim  at  simplicity  of  effect.  This  will 
render  imperfect  execution  agreeable,  but  what  is  elab- 
orate must  be  skilful  to  please. 

As  the  light  comes  in  one  direction,  the  picture  will 
have  a  light  and  a  shadow  side.  Be  careful  not  to  dis- 
turb the  shadow  side  by  introducing  into  it  bright  lights, 
but  let  the  light  parts  of  this  side  be  of  a  darker  tint 
than  some  of  the  shadows  on  the  other.  Determine  on 
the  disposition  of  your  light  and  shade  before  you  com- 
mence, and  pass  a  tint  over  that  part  of  your  picture 
designed  to  be  in  shadow.  This  will  secure  you  from 
leaving  bright  lights  here,  and  produce  breadth  of  effect. 

Objects  situate  between  the  eye  and  the  light,  look 
dark.  The  sail  of  a  vessel,  so  placed,  looks  darker 
than  the  sky  or  the  water.  A  tree  in  the  foreground, 
with  a  similar  disposition  of  light,  may  receive  a  deep 
tint,  and  contrasts  finely  with  the  sky  and  the  lights 
which  catch  on  the  distance  or  nearer  objects. 

A  landscape  usually  looks  best  in  a  morning  or  even- 
ing light,  when  the  shadows  are  long. 

On  many  accounts,  India  ink  is  the  most  suitable 
medium  for  a  beginner  to  use  in  finishing  up  a  sketch. 
Having  disposed  the  light  and  shade,  as  directed  above, 
begin  with  a  hght  tint  (your  pencil  being  well  filled 
with  the  colour)  and  make  out  the  sky,  doing  the  clouds 
first,  let  these  assume  generally  a  horizontal  charac- 
ter. Next  put  in  the  blue  sky,  leaving  out  the  lighter 
edges  of  the  clouds.    This  you  will  do  with  more  grace 


* 


66  LESSONS  IN  PERSPECTIVE. 

and  freedom  if  the  cloud  is  already  designed.  With 
the  same  light  tint,  pass  over  the  mountains  or  any  dis- 
tant parts,  leaving  out  such  lights  as  the  sun,  striking  on 
the  hills,  buildings  or  water,  would  produce.  Cover 
every  other  part  of  the  picture  with  this  tint,  except  the 
brightest  lights  of  the  foreground.  Then  take  a  tint 
somewhat  darker,  and  finish  those  parts  next  the  most 
distant ;  carry  down  this  tint  like  the  first,  over  every 
other  part  of  the  picture,  leaving  out  such  parts  only  as 
are  to  be  lighter  than  the  tint  in  your  pencil,  and  so 
proceed  with  as  many  tints  as  you  have  distances. 

If  the  distant  parts  look  too  strong,  pass  a  sponge 
wet  with  pure  water,  over  them ;  this  will  give  them 
softness.  When  you  commence,  after  having  made  the 
outline,  wet  the  paper  with  a  sponge,  and  press  it  with 
a  cloth  or  blotting  paper.  This  gives  a  little  dampness, 
which  makes  the  ink  work  favourably. 

With  regard  to  fohage  it  m^ay  be  observed,  that  the 
more  distant  it  is,  the  less  distinct  and  the  smaller  is  the 
character  of  its  touch.  Each  tree  should  have  a  touch 
of  its  own,  by  which  its  species  is  expressed.  A  hill 
covered  with  foliage  is  represented  by  a  touch  which 
resembles  a  set  of  curves  with  indented  edges  ;  the 
more  distant  such  foliage  is,  the  nearer  the  curve  ap- 
proaches a  horizontal  character,  and  the  closer  are  the 
lines  or  touches. 


END. 


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